Roman Fric

Born 1944 in Presov, district Presov.
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- Math. Inst. Slovak Acad. Sci., Extension in Kosice (since 1994 Principal Research Fellow)
and
2000- 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:

• Fric, R., A note on Frechet spaces.
  Comment. Math. Univ. Carolin. 13 (1972), 411--418.
• 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.
• Fric, R., Further note on Frechet spaces.
  Comment. Math. Univ. Carolin. 14 (1973), 661--667.
• 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.
• 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.
• 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.
• 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.
• Fric, R., Regularity and extension of mappings in sequential spaces.
  Comment. Math. Univ. Carolin. 15 (1974), 161--171.
• Fric, R., Extension of sequentially continuous mappings.
  Comment. Math. Univ. Carolin. 16 (1975), 273--276.
• 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.
• Fric, R., On E-sequentially regular spaces.
  Czechoslovak Math. J. 26 (1976), 604--612.
• Fric, R., On convergence spaces and groups.
  Math. Slovaca 27 (1977), 323--330.
• Fric, R., Kent, D. C., Completion of sequential Cauchy spaces.
  Comment. Math. Univ. Carolin. 18 (1977), 351--261.
• 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.
• 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.
• Fric, R., Kent, D. C., On the natural completion functor for Cauchy spaces.
  Bull. Austral. Math. Soc. 19 (1978), 335--343.
• Fric, R., Kent, C. D., Completion functors for Cauchy spaces.
  Internat. J. Math. Math. Sci. 2 (1979), 589--604.
• Fric, R., Koutnik, V., Sequentially complete spaces.
  Czechoslovak Math. J. 29 (1979), 287--297.
• Fric, R., Piatka, L., Continuous homomorphisms in set algebras.
  Prace Stud. Vys. Sk. Doprav. Ziline Ser. Mat.-fyz., 2 (1979), 13--20. (Slovak)
• 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.
• 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.
• Fric, R., On the sequential envelopes of convergence groups.
  Prace stud. Vysokej skoly doprav., Zilina, Ser. Mat.-Fyz. 2 (1980), 7--11.
• 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.
• Fric, R., Kent, D. C., Completion of pseudo-topological groups.
  Math. Nachr. 99 (1980), 99--103.
• 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.
• 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.
• 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.
• 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.
• 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.
• Fric, R., Kent, D. C., A completion functor for Cauchy groups.
  Internat. J. Math. Math. Sci. 4 (1981), 55--65.
• Fric, R., Gavalec, M., On the Novak completion of convergence groups.
  Comment. Math. univ. Carolin. 24 (1983), 341--347.
• Fric, R., Husek, M., Projectively generated convergence of sequences.
  Czechoslovak Math. J. 33 (1983), 525--536.
• 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.
• 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.
• 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.
• 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.
• Fric, R., Novak, J., A tiny peculiar Frechet space.
  Czechoslovak Math. J. 34 (1984), 22--27.
• 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.
• 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.
• Fric, R., An example of a self-dual convergence group.
  Prace stud. Vysokej skoly Doprav., Zilina, Ser. Mat.-Fyz. 5 (1985), 7--9.
• 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.
• 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.
• 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.
• 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.
• Fric, R., Zanolin, F., Fine convergence in free groups.
  Czechoslovak Math. J. 36 (1986), 134--139.
• Fric, R., Zanolin, F., Sequential convergence in free groups.
  Rend. Istit. Matem. Univ. Trieste 18 (1986), 200--218.
• Fric, R., Dikranjan, D., F. Zanolin, F., On convergence groups having dense coarse subgroups.
  Czechoslovak Math. J. 37 (1987), 471--479.
• Fric, R., Products of coarse convergence groups.
  Czechoslovak Math. J. 38 (1988), 285--290.
• Fric, R., Remarks on sequential envelopes.
  Rend. Istit. Mat. Univ. Trieste 20 (1988), 19--28.
• 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.
• Fric, R., Zan, S., A note on diagonal and matrix properties of convergence spaces.
  Math. Slovaca 38 (1988), 171--176.
• Fric, R., Rationals with exotic convergences.
  Math. Slovaca 39 (1989), 141--147.
• 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.
• Fric, R., Cauchy sequences in L-groups.
  Czechoslovak Math. J. 40 (1990), 25--30.
• Fric, R., On plane topologies with high sequential order.
  Comment. Math. Univ. Carolin. 31 (1990), 33--36.
• Fric, R., Rationals with exotic convergence II.
  Math. Slovaca 40 (1990), 389-400.
• Fric, R., Some results in sequential convergence groups.
  In: Generalized Functions and Convergence. World Scientific Publishing Co., Singapore, 1990, 311--334.
• Fric, R., Zanolin, F., Coarse sequential convergence in groups, etc.
  Czechoslovak Math. J. 40 (1990), 459--467.
• Fric, R., Kent, D. C., The finite product theorem for certain epireflections.
  Math. Nachr. 150 (1991), 7--14.
• Fric, R., On ring convergences.
  Riv. Mat. Pura Appl. 11 (1992), 125--138.
• 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.
• Fric, R., Gerlits, J., On the sequential order.
  Math. Slovaca 42 (1992), 505--512.
• Fric, R., Kent, D. C., Regular spaces and extension of maps.
  Math. Slovaca 42 (1992), 349--357.
• Fric, R., Kent, D. C., Regular L-spaces.
  Czechoslovak Math. J. 42 (1992), 475--486.
• Fric, R., Koutnik, V., Sequential convergence spaces: iteration, extension, completion, enlargement.
  In: Recent progress in General Topology, North Holland, Amsterdam 1992, 199--213.
• Fric, R., Zanolin, F., Strict completions of L_0^*-groups.
  Czechoslovak Math. J. 42 (1992), 589--598.
• Fric, R., L-groups versus k-groups.
  Math. Bohemica 118 (1993), 113--121.
• 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.
• 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.
• Fric, R., On limits without epsilons.
  Real Anal. Exchange 19 (1993-94), 129--134.
• Fric, R., On strict extensions.
  In: Topology with Applications, Szekszard 1993 (Hungary), Bolyai Society Mathematical Studies 4 (1995), 223--232.
• Fric, R., Group hyperreals: iterated sequential completions of rationals.
  Tatra Mt. Math. Publ. 5 (1995), 89--96.
• Fric, R., Convergence and numbers.
  Topology and its Applications 70 (1996), 139--146.
• Fric, R., Kemoto, N., Sequential envelope revisited.
  Abstracts of the Eighth Prague Topological Symposium, Part B: Extended abstracts, Praha 1996, 126--134.
• Fric, R., Stone-type duality and its applications to probability.
  Topology Proc. 22, Summer 1997, 125--137.
• 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.
• 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.
• Fric, R., Zanolin, F., Relatively coarse sequential convergence.
  Czechoslovak Math. J. 47 (1997), 395--408.
• Fric, R., Topology versus sequential convergence.
  Filomat 12 (1998), 1--12.
• Fric, R., Borsik, J., Pointwise convergence fails to be strict.
  Czechoslovak Math. J. 48 (1998), 313--320.
• Fric, R., Nogura, T., Rings of maps: sequential convergence and strictness.
  Tatra Mt. Math. Publ. 24 (1998), 137--143.
• Fric, R., Rings of maps: sequential convergence and completion.
  Czechoslovak Math. J. 49 (1999), 111--118.
• 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.
• Fric, R., Kemoto, N., Sequential completeness of subspaces of products of two cardinals.
  Czechoslovak Math. J. 49 (1999), 118--125.
• Fric, R., On observables.
  Internat. J. Theoret. Phys. 39 (2000), 677--686.
• 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.
• Fric, R., Boolean algebras: convergence and measure.
  Topology and its Applications 111 (2001), 139--149.
• Fric, R., Jakubik, J., Sequential convergence on Boolean algebras defined by systems of maximal filters.
  Czechoslovak Math. J. 51 (2001), 261--274.
• Fric, R., Lukasiewicz tribes are absolutely sequentially closed bold algebras.
  Czechoslovak Math. J. 52 (2002), 861--874.
• Fric, R., Measures on MV-algebras.
  Soft Computing 7 (2002), 130--137
• Fric, R., Convergence and duality.
  Appl. Categorical Structures 10 (2002), 257--266.
• Fric, R., Duality for generalized events.
  Math. Slovaca 54 (2004), 49--60.
• Fric, R., Coproducts of D-posets and their application to probability.
  Internat. J. Theoret. Phys. 43 (2004), 1625--1632
• Fric, R., Remarks on statistical maps and fuzzy (operational) random variables.
  Tatra Mt. Math. Publ. 30 (2005), 21--34.
• Fric, R., Extension of measures: a categorical approach.
  Math. Bohemica 130 (2005), 397--407.
• Fric, R., Statistical maps: a categorical approach.
  Math. Slovaca 57 (2007), 41--57.