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Roman Frič

30. 9. 1944 (Prešov) – 13. 1. 2021 (Košice)

University studies:
Charles University Prague, School of Mathematics and Physics (major field: Probability and Statistics) 1962 – 1967.
RNDr. 1972, CSc. (PhD, advisor Prof. Josef Novak) 1972, Docent 1993, DrSc. 1995
Positions held:
1966 – 1968 Math. Inst. Czechoslovak Acad. Sci. Praha (part time);
1968 – 1972 Math. Inst. Czechoslovak Acad. Sci. Praha (Sci. Fellow);
1972 – 1979 Technical University of Transport Engineering in Zilina (Assistant Prof.);
1979 – 2021 Math. Inst. Slovak Acad. Sci., Extension in Kosice (since 1994 Principal Research Fellow);
2000 – 2016 Catholic University in Ruzomberok (associate professor).
Visiting Positions:
University of P. J. Safarik in Kosice; Washington State University, Pullman, USA; Bourgogne University, Dijon, France; University Udine, Italy;
Study Stays: USA (IREX, 1974–75, 6 months); Italy (C.N.R., 1986, 1988, 1990, 2+2+1 months); Japan (JSPS, 1996, 2 months); UK (British Council – Cambridge Hospitality Scheme, 1997, 1 month);
Field of Interest: Quantum and Fuzzy Structures, Probability (Foundations), General Topology (Convergence Structures).

List of Publications:

  1. Fric, R., A note on Frechet spaces, Comment. Math. Univ. Carolin. 13 (1972), 411–418.
  2. Fric, R., Sequential envelope and subspaces of the Cech-Stone compactification. In: General Topology and its Relations to Modern Analysis and Algebra, III (Proc. Third Prague Topological Sympos., 1971), 123–126. Academia, Prague, 1972.
  3. Fric, R., Further note on Frechet spaces, Comment. Math. Univ. Carolin. 14 (1973), 661–667.
  4. Fric, R., On the sequential uniform structures of A. Goetz, In: Proceedings of the International Symposium on Topology and its Applications (Budva, 1972), 90–93. Savez Drustava Mat. Fiz. i Astronom., Belgrade, 1973.
  5. Fric, R., On the completion of sequential structures, In: Proceedings of the International Symposium on Topology and its Applications (Budva, 1972), 94–96. Savez Drustava Mat. Fiz. i Astronom., Belgrade, 1973.
  6. Fric, R., On a problem of J. Novak, In: Topics in Topology (Proc. Colloq. Keszthely, 1972), 317–319. Colloq. Math. Soc. Janos Bolyai 8, North-Holland, Amsterdam, 1974.
  7. Fric, R., On the sequential envelope of products, In: Fourth Scientific Conference, College of Transport Engineering, Zilina, Section 1: Mathematics, Physics, Cybernetics, 89–92. Vysoka skola dopravna v Ziline, Zilina, 1974.
  8. Fric, R., Regularity and extension of mappings in sequential spaces, Comment. Math. Univ. Carolin. 15 (1974), 161–171.
  9. Fric, R., Extension of sequentially continuous mappings, Comment. Math. Univ. Carolin. 16 (1975), 273–276.
  10. Fric, R., On continuous characters of Borel sets, In: Proceedings of the Conference on Convergence Spaces (Univ. Nevada, Reno, Nev., 1976), 35–44. Dept. Math. Univ. Nevada, Reno, Nev., 1976.
  11. Fric, R., On E-sequentially regular spaces, Czechoslovak Math. J. 26 (1976), 604–612.
  12. Fric, R., On convergence spaces and groups, Math. Slovaca 27 (1977), 323–330.
  13. Fric, R., Kent, D. C., Completion of sequential Cauchy spaces, Comment. Math. Univ. Carolin. 18 (1977), 351–261.
  14. Fric, R., Koutnik V., Sequentially complete spaces, In: General Topology and its Relations to Modern Analysis and Algebra, IV. (Proc. Fourth Prague Topological Sympos., Prague, 1976), Part B, 127–131. Soc. Czech. Mathematicians and Physicists, Prague, 1977.
  15. Fric, R., Sequential completeness versus Cech-completeness, In: Sixth Winter School on Abstract Analysis held January 28 – February 11, 1978, 35–36. Mathematical Institute of the Czechoslovak Academy of Sciences, Praha, 1978.
  16. Fric, R., Kent, D. C., On the natural completion functor for Cauchy spaces, Bull. Austral. Math. Soc. 19 (1978), 335–343.
  17. Fric, R., Kent, C. D., Completion functors for Cauchy spaces, Internat. J. Math. Math. Sci. 2 (1979), 589–604.
  18. Fric, R., Koutnik, V., Sequentially complete spaces, Czechoslovak Math. J. 29 (1979), 287–297.
  19. Fric, R., Piatka, L., Continuous homomorphisms in set algebras, Prace Stud. Vys. Sk. Doprav. Ziline Ser. Mat.-fyz., 2 (1979), 13–20. (Slovak)
  20. Fric, R., On completion of Cauchy spaces, In: Proceedings of the Conference on Convergence (Szczyrk, 1979), 24–28. Polsk. Akad. Nauk, Oddzial v Katowiciach, Katowice, 1980.
  21. Fric, R., On sequential Cauchy spaces, In: Proceedings of the Conference on Convergence Structures (Cameron Univ. Lawton, Okla., 1980), 56–61. Cameron Univ., Lawton, Okla., 1980.
  22. Fric, R., On the sequential envelopes of convergence groups, Prace stud. Vysokej skoly doprav., Zilina, Ser. Mat.-Fyz. 2 (1980), 7–11.
  23. Fric, R., Husek, M., Epireflective subcategories of convergence spaces, In: Eighth Winter School on Abstract Analysis held January 27 – February 10, 1980, 68–72. Mathematical Institute of the Czechoslovak Academy of Sciences, Praha, 1980.
  24. Fric, R., Kent, D. C., Completion of pseudo-topological groups, Math. Nachr. 99 (1980), 99–103.
  25. Fric, R., Kent, D. C., On c-embedded sequential convergence spaces, In: Convergence structures and applications to Analysis (Frankfurt/Oder, 1978), Abh. Akad. Wiss. DDR, Abt. Math.-Naturwiss.-Technik, 1979, Nr. 4N, 33–36. Akademie-Verlag, Berlin, 1980.
  26. Fric, R., Kent, D. C., On functiorial completions of Cauchy spaces, In: Topology (Proc. Fourth Colloq., Budapest, 1978), Vol. I, 443–440. Colloq. Math. Soc. Janos Bolyai 23, North-Holland, Amsterdam, 1980.
  27. Fric, R., Koutnik, V., Sequential points of beta X, In: Topology (Proc. Fourth Colloq., Budapest, 1978), Vol. I, 443–440. Colloq. Math. Soc. Janos Bolyai 23, North-Holland, Amsterdam, 1980.
  28. Fric, R., Koutnik, V., Sequential structures, In: Convergence structures and applications to analysis (Frankfurt/Oder, 1978), Abh. Akad. Wiss. DDR, Abt. Math.-Naturwiss.-Technik, 1979, Nr. 4N, 37–56. Akademie-Verlag, Berlin, 1980.
  29. Fric, R., McKennon, K., Richardson, S. D., Sequential convergence in C(X), In: Convergence structures and applications to analysis (Frankfurt/Oder, 1978), Abh. Akad. Wiss. DDR, Abt. Math.-Naturwiss.-Technik, 1979, Nr. 4N, 57–65. Akademie-Verlag, Berlin, 1980.
  30. Fric, R., Kent, D. C., A completion functor for Cauchy groups, Internat. J. Math. Math. Sci. 4 (1981), 55–65.
  31. Fric, R., Gavalec, M., On the Novak completion of convergence groups, Comment. Math. univ. Carolin. 24 (1983), 341–347.
  32. Fric, R., Husek, M., Projectively generated convergence of sequences, Czechoslovak Math. J. 33 (1983), 525–536.
  33. Fric, R., Kent, D. C., A nice completion need not be strict, In: General Topology and its Relations to Modern Analysis and Algebra, V (Prague, 1981), 189–192. Sigma Ser. Pure Math. J., Heldermann, Berlin, 1983.
  34. Fric, R., Koutnik, V., Sequential convergence since Kanpur conference, In: General Topology and its Relations to Modern Analysis and Algebra, V (Prague, 1981), 193–205. Sigma Ser. Pure Math. J., Heldermann, Berlin, 1983.
  35. Fric, R., Four questions concerning constructions of convergence groups, In: Proc. Conf. Convergence and Generalized Functions (Katowice, 1983), 20–24. Polsk. Akad. Nauk, Katowice, 1984.
  36. Fric, R., Koutnik, V., Recent development in sequential convergence, In: Cnvergence Structures and Applications II (Schwerin, 1983), Abh. Akad. Wiss. DDR, Abt. Math.-Naturwiss.-Technik, 1984, Nr. 2N, 37–46. Akademie-Verlag, Berlin, 1984.
  37. Fric, R., Novak, J., A tiny peculiar Frechet space, Czechoslovak Math. J. 34 (1984), 22–27.
  38. Fric, R., Vojtas, P., Convergent sequences in beta X, In: Proceedings of the 11th Winter School (Zelezna Ruda, 1983), Rend. Circ. Mat. Palermo 2 (1984), Suppl. no. 3, 133–137.
  39. Fric, R., Zanolin, F., A convergence group having no completion, In: Convergence Structures and Applications II (Schwerin, 1983), Abh. Akad. Wiss. DDR, Abt. Math.-Naturwiss.-Technik, 1984, Nr. 2N, 47–48. Akademie-Verlag, Berline, 1984.
  40. Fric, R., An example of a self-dual convergence group, Prace stud. Vysokej skoly Doprav., Zilina, Ser. Mat.-Fyz. 5 (1985), 7–9.
  41. Fric, R., Vojtas, P., Diagonal conditions in sequential convergence, In: Convergence Structures 1984 (Proc. Conf. on Convergence, Bechyne, 1984), 77–94. Akademie-Verlag, Mathematical Research/Mathematische Forschung Bd. 24, Berlin, 1985.
  42. Fric, R., Vojtas, P., The space ^omega omega in sequential convergence, In: Convergence Structures 1984 (Proc. Conf. on Convergence, Bechyne, 1984), 95–106. Akademie-Verlag, Mathematical Research/Mathematische Forschung Bd. 24, Berlin, 1985.
  43. Fric, R., Zanolin, F., Coarse convergence groups, In: Convergence Structures 1984 (Proc. Conf. on Convergence, Bechyne, 1984), 107–114. Akademie-Verlag, Mathematical Research/Mathematische Forschung Bd. 24, Berlin, 1985.
  44. Fric, R., Zanolin, F., Remarks on sequential convergence in free groups, In: Topology and Applications (Eger, 1983), Colloq. Math. Soc. Janos Bolyai 41, 283–291. North-Holland, Amsterdam, 1986.
  45. Fric, R., Zanolin, F., Fine convergence in free groups, Czechoslovak Math. J. 36 (1986), 134–139.
  46. Fric, R., Zanolin, F., Sequential convergence in free groups, Rend. Istit. Matem. Univ. Trieste 18 (1986), 200–218.
  47. Fric, R., Dikranjan, D., F. Zanolin, F., On convergence groups having dense coarse subgroups, Czechoslovak Math. J. 37 (1987), 471–479.
  48. Fric, R., Products of coarse convergence groups, Czechoslovak Math. J. 38 (1988), 285–290.
  49. Fric, R., Remarks on sequential envelopes, Rend. Istit. Mat. Univ. Trieste 20 (1988), 19–28.
  50. Fric, R., Koutnik, V., Completions of convergence groups, In: General Topology and its Relations to Modern Analysis and Algebra, VI (Proc. Sixth Prague topological Sympos., 1986), 187–201. Heldermann Verlag, Berlin, 1988.
  51. Fric, R., Zan, S., A note on diagonal and matrix properties of convergence spaces, Math. Slovaca 38 (1988), 171–176.
  52. Fric, R., Rationals with exotic convergences, Math. Slovaca 39 (1989), 141–147.
  53. Fric, R., Koutnik, V., Completions for subcategories of convergence rings, In: Categorical Topology and its Relations to Modern Analysis, Algebra and Combinatorics. World Scientific Publishing Co., Singapore, 1989, 195–207.
  54. Fric, R., Cauchy sequences in L-groups, Czechoslovak Math. J. 40 (1990), 25–30.
  55. Fric, R., On plane topologies with high sequential order, Comment. Math. Univ. Carolin. 31 (1990), 33–36.
  56. Fric, R., Rationals with exotic convergence II, Math. Slovaca 40 (1990), 389–400.
  57. Fric, R., Some results in sequential convergence groups, In: Generalized Functions and Convergence. World Scientific Publishing Co., Singapore, 1990, 311–334.
  58. Fric, R., Zanolin, F., Coarse sequential convergence in groups, etc., Czechoslovak Math. J. 40 (1990), 459–467.
  59. Fric, R., Kent, D. C., The finite product theorem for certain epireflections, Math. Nachr. 150 (1991), 7–14.
  60. Fric, R., On ring convergences, Riv. Mat. Pura Appl. 11 (1992), 125–138.
  61. Fric, R., On completions of rationals, In: Recent developments of General Topology and its Applications. Math. Research, No. 67, Akademie-Verlag, Berlin 1992, 124–129.
  62. Fric, R., Gerlits, J., On the sequential order, Math. Slovaca 42 (1992), 505–512.
  63. Fric, R., Kent, D. C., Regular spaces and extension of maps, Math. Slovaca 42 (1992), 349–357.
  64. Fric, R., Kent, D. C., Regular L-spaces, Czechoslovak Math. J. 42 (1992), 475–486.
  65. Fric, R., Koutnik, V., Sequential convergence spaces: iteration, extension, completion, enlargement, In: Recent progress in General Topology, North Holland, Amsterdam 1992, 199–213.
  66. Fric, R., Zanolin, F., Strict completions of L_0^*-groups, Czechoslovak Math. J. 42 (1992), 589–598.
  67. Fric, R., L-groups versus k-groups, Math. Bohemica 118 (1993), 113–121.
  68. Fric, R., Husek, M., Koutnik, V., Sequential groups, k-groups and other categories of continuous algebras, In: Topology, (Pecs, Hungary, 1989). Colloquia Mathematica Societatis Janos Bolyai 55, Amsterdam, North-Holland, 1993, 223–232.
  69. Fric, R., Kent, D. C., Regularity and sequential convergence spaces, In: Papers on General Topology and Applications, Annals of the New York Academy of Sciences, Vol. 704 129–134. (Seventh Summer Conference at the University of Wisconsin, 1991). Editors: Andima, S. et al., New York, 1993.
  70. Fric, R., On limits without epsilons, Real Anal. Exchange 19 (1993-94), 129–134.
  71. Fric, R., On strict extensions, In: Topology with Applications, Szekszard 1993 (Hungary), Bolyai Society Mathematical Studies 4 (1995), 223–232.
  72. Fric, R., Group hyperreals: iterated sequential completions of rationals, Tatra Mt. Math. Publ. 5 (1995), 89–96.
  73. Fric, R., Convergence and numbers, Topology and its Applications 70 (1996), 139–146.
  74. Fric, R., Kemoto, N., Sequential envelope revisited, Abstracts of the Eighth Prague Topological Symposium, Part B: Extended abstracts, Praha 1996, 126–134.
  75. Fric, R., Stone-type duality and its applications to probability, Topology Proc. 22, Summer 1997, 125–137.
  76. Fric, R., History of sequential convergence spaces, In: Handbook of the History of General Topology, Volume 1, 343–355. Editors: C. E. Aull and R. Lowen, Kluwer Academic Publishers, Amsterdam, 1997.
  77. Fric, R., Sequential structures and probability: categorical reflections, In: Categorical Methods in Algebra and Topology (A collection of papers in honour of Horst Herrlich), Mathematik-Arbeitspapiere 48, 157–169. Editor: H.-E. Porst, Universitat Bremen, Bremen, 1997.
  78. Fric, R., Zanolin, F., Relatively coarse sequential convergence, Czechoslovak Math. J. 47 (1997), 395–408.
  79. Fric, R., Topology versus sequential convergence, Filomat 12 (1998), 1–12.
  80. Fric, R., Borsik, J., Pointwise convergence fails to be strict, Czechoslovak Math. J. 48 (1998), 313–320.
  81. Fric, R., Nogura, T., Rings of maps: sequential convergence and strictness, Tatra Mt. Math. Publ. 24 (1998), 137–143.
  82. Fric, R., Rings of maps: sequential convergence and completion, Czechoslovak Math. J. 49 (1999), 111–118.
  83. Fric, R., Dikranjan, D., Minimality with respect to a bireflector: T-minimal and v-coarse groups, In: Symposium on Categorical Topology (Rondebosh, 1994), 75–87, Univ. Cape Town, Rondebosh, 1999.
  84. Fric, R., Kemoto, N., Sequential completeness of subspaces of products of two cardinals, Czechoslovak Math. J. 49 (1999), 118–125.
  85. Fric, R., On observables, Internat. J. Theoret. Phys. 39 (2000), 677–686.
  86. Fric, R., MV-algebras: convergence and duality, In: Categorical Methods in Algebra and Topology (Proceedings of the Conference CatMAT 2000), Mathematik-Arbeitspapiere 54, 169–179. Editors: H. Herrlich and H.-E. Porst), Universitat Bremen, Bremen, 2000.
  87. Fric, R., Boolean algebras: convergence and measure, Topology and its Applications 111 (2001), 139–149.
  88. Fric, R., Jakubik, J., Sequential convergence on Boolean algebras defined by systems of maximal filters, Czechoslovak Math. J. 51 (2001), 261–274.
  89. Fric, R., Lukasiewicz tribes are absolutely sequentially closed bold algebras, Czechoslovak Math. J. 52 (2002), 861–874.
  90. Fric, R., Measures on MV-algebras, Soft Computing 7 (2002), 130–137
  91. Fric, R., Convergence and duality, Appl. Categorical Structures 10 (2002), 257–266.
  92. Fric, R., Duality for generalized events, Math. Slovaca 54 (2004), 49–60.
  93. Fric, R., Coproducts of D-posets and their application to probability, Internat. J. Theoret. Phys. 43 (2004), 1625–1632
  94. Fric, R., Remarks on statistical maps and fuzzy (operational) random variables, Tatra Mt. Math. Publ. 30 (2005), 21–34.
  95. Fric, R., Extension of measures: a categorical approach, Math. Bohemica 130 (2005), 397–407.
  96. Fric, R., Statistical maps: a categorical approach, Math. Slovaca 57 (2007), 41–57.
  97. Fric, R., Duality: random variables versus observables, In: Annales Academiae Pedagogicae Cracoviensis, Studia Mathematica, Editor: A. Płocki, vol. 3. Krakow, Wydawnictwo Naukowe Akademii Pedagogycznej, 2003. pp. 55–60.
  98. Fric, R., Nonelementary Notes on Elementary Events, In: Matematyka IX prace naukowe. WSP, Czestochowa : 2003. 137 –141.
  99. Fric, R., Products and Projections, In: Mathematica, Proceedings of the XIth Slovak-Polish-Czech Mathematical School. PF KU, Ružomberok : 2004, 103–107.
  100. Fric, R., Kvantové štruktúry a teória kategórií, Advances in Electrical and Electronic Engineering 3 (2004), 14–20.
  101. Fric, R., Remarks on metrics, In: XIIth Czech-Polish-Slovak Mathematical School (Proceedings ot the XIIth Czech-Polish-Slovak Mathematical School, Hluboš, June 2 – 4, 2005), Faculty of Education, University J. E. Purkyně in Ústí nad Labem, Ústí nad Labem : 2005. 26–28.
  102. Fric, R., Papco, M., Fuzzy random variables, In: APLIMAT 2006, 5th International Conference, STU Bratislava : 2006, 511–516.
  103. Fric, R., Papco, M., Triangular structures and duality, In: Scientific Issues, Mathematics XII, Jan Dlugosz University of Czestochowa, Czestochowa : 2007. 23–28.
  104. Fric, R., Extension od domains of states, Soft Computing, 12 (2008), 373–379.
  105. Fric, R., Measures: continuity, measurability, duality, extension, Tatra Mt. Math. Publ. 42 (2009), 161–174.
  106. Fric, R., Papco, M., On probability domains, Internat. J. Theoret. Phys. 49 (2010), 3092–3100.
  107. Chovanec, F., Fric, R., States as morphisms, Internat. J. Theoret. Phys. 49 (2010), 3050–3060.
  108. Fric, R., Simplex-valued probability, Math. Slovaca 60 (2010), 607–614.
  109. Fric, R., Papco, M., A categorical approach to probability theory, Studia Logica 94 (2010), 215–230.
  110. Fric, R., Papco, M., Fuzzification of crisp domains, Kybernetika 46 (2010), 1009–1024.
  111. Fric, R., Papco, M., Random variable as a network of pipelines Usta ad Albim Bohemica 10 (2010), 33–38.
  112. Fric, R., States on bold algebras: Categorical aspects, J. Logic Computation 21 (2011), 465–477.
  113. Fric, R., Papco, M., On probability domains II, Internat. J. Theoret. Phys. 50 (2011), 3778–3786.
  114. Fric, R., Papco, M., Random walk – fuzzy aspects, In: Scientific Issues, Mathematics XVI, Jan Dlugosz University of Czestochowa, Czestochowa, 2011, 205–212.
  115. Fric, R., From probability to sequences and back, Rend. Instit. Mat. Univ. Trieste 44 (2012), 1–12.
  116. Fric, R., Random variables – opening a random black box, In: Matematyka w przyrodze i sztuce – matematyka, przyroda i sztuka w ksztalceniu powszechnym, 2012, Nowy Sacz, 215–219.
  117. Fric, R., Upgrading probability: what we can learn from History?, In: Proceedings of the Conference on the History of Mathematics and Teaching of Mathematics, Sarospatak, May 24–26, 2012(ed. Peter Kortesi), 2012, Miskolc.
  118. Fric, R., Mathematics of exceptions. In: Matematyka w przyrodzie – matematyka i przyroda w kształceniu powszechnym, PWSZ Nowy Sącz 2011, p. 13–18.
  119. Fric, R., On D-posets of fuzzy sets, Math. Slovaca 64 (2014), No. 3, 545–554.
  120. Fric, R. Papco, M., Fuzzified probability: from Kolmogorov to Zadeh and beyond, In: Scientific Issues, Jan Długosz University in Czestochowa, Mathematics XIX , 2014, 175–184.
  121. Fric, R., Papco, M., On probability domains III, Internat. J. Theoret. Phys. 54 (2015), 4236–4246.
  122. Skrivanek, V., Fric, R., Generalized random events, Internat. J. Theoret. Phys. 54 (2015), 4386–4396.
  123. Fric, R., Papco, M., Upgrading probability via fractions of events, Commun. Math. 24 (2016), 29–41.
  124. Fric, R., Papco, M., Probability: from classical to fuzzy, Fuzzy Sets Syst. 326 (2017), 106–114.
  125. Elias, P., Fric, R., Factorization of observables, Internat. J. Theoret. Phys. 56 (2017), No. 12, 4073–4083.
  126. Fric, R., Papco, M., On probability domains IV, Internat. J. Theoret. Phys. 56 (2017), No. 12, 4084–4091.
  127. Babicova, D., Fric, R., Real functions in stochastic dependence. Tatra Mountains Mathematical Publ. 74 (2019), 17–34.
  128. Fric, R., Products of measurable spaces and applications. Tatra Mountains Mathematical Publ. 74 (2019), 47–56.
  129. Elias, P., Fric, R., Conditional probability on full Lukasiewicz tribes, Soft Computing 24 (2020), 6521–6529.
  130. Fric, R., Elias, P., Papco, M., Divisible extension of probability, Mathematica Slovaca 70 (2020), 1445–1456.