A.  Areas of interest

Topology: point-set, geometric, point-set lattice-theoretic (poslat)
Foundations: foundations of topology and fuzzy logic—point-set, lattice-theoretic, categorical methods
Examples: "canonical" examples of poslat topological spaces
Probability: probability axiomatics

          B.  List of Publications and Ongoing Work
Works in progress

[1] Axiomatic foundations for fuzzy (quasi-)uniform spaces using uniform coverings.
[2] A measure-theoretic approach to fuzzy subsethood operators, joint-work with V. Dimitrijevic.
[3] Comparison of localic and fuzzy topological products.

Works in print

[4] Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, 1999, Handbooks of Fuzzy Sets: Volume 3, Kluwer Academic Publishers (Dordrecht), 716 pages, co-editor with U. Höhle.
[5] Powerset operator foundations for poslat set theories and topologies, Handbooks of Fuzzy Sets Series 3(1999) 91–116, Kluwer Academic Publishers (Dordrecht).
[6] Categorical foundations for variable-basis fuzzy topology, Handbooks of Fuzzy Sets Series 3(1999) 273–388, Kluwer Academic Publishers (Dordrecht).
[7] Separation axioms: representation theorems, compactness, and compactifications, Handbooks of Fuzzy Sets Series 3(1999) 481–552, Kluwer Academic Publishers (Dordrecht).
[8] Fuzzy real lines and dual real lines as poslat topological, uniform, and metric ordered semirings with unity, Handbooks of Fuzzy Sets Series 3(1999) 607–632, Kluwer Academic Publishers (Dordrecht).
[9] Topological and Algebraic Structures: Abstracts of Twentieth Linz Seminar, Fuzzy Logic Laboratorium Linz (Hagenberg) / Institüt für Algebra, Stochastik, und Wissenbasierte Mathematische Systeme / Johannes Kepler Universität (Linz), 52 page, co-editor with E. P. Klement.
[10] Variable basis fuzzy topology and compactifications: a status report, Topological and Algebraic Structures (1999) 34–35, Abstracts of the Twentieth Linz Seminar, Fuzzy Logic Laboratorium Linz (Hagenberg) / Institüt für Algebra, Stochastik, und Wissenbasierte Mathematische Systeme / Johannes Kepler Universität (Linz).
[11] Covering/Hutton fuzzy uniformities: preliminary remarks,Topological and Algebraic Structures (1999) 52, Abstracts of the Twentieth Linz Seminar, Fuzzy Logic Laboratorium Linz (Hagenberg) / Institüt für Algebra, Stochastik, und Wissenbasierte Mathematische Systeme / Johannes Kepler Universität (Linz).
[12] Powerset operator based foundation for point-set lattice-theoretic (poslat) set theories and topologies, Quaestiones Mathematicae20(3)(1997) 463–530.
[13] Special Issue on Fuzzy Topology, Fuzzy Sets and Systems 73(1995) 1–183, co-editor with U. Höhle and A. Šostak.
[14] Applications of localic separation axioms, compactness axioms, representations, and compactifications to poslat topological spaces, Fuzzy Sets and Systems 73(1995) 55–87.
[15] Necessity of Chang-Goguen Topologies, Rendiconti Cir. Mat. Palermo (Suppl.) Series II 29(1992) 299–314.
[16] Applications of Category Theory to Fuzzy Subsets, 1992, Kluwer Academic Publishers (Dordrecht), 398 page, co-editor with E. P. Klement and U. Höhle.
[17] Categorical frameworks for Stone Representation Theories, in Applications of Category Theory to Fuzzy Subsets, 1992, Kluwer Academic Publishers (Dordrecht), 177–232.
[18] Roundtable: model-theoretic vis-a-vis non-model-theoretic fuzzy set theories, Applications of Category Theory to Fuzzy Subsets, 1992, Kluwer Academic Publishers (Dordrecht), 59–67.
[19] Roundtable: open questions in logic and topology, Applications of Category Theory to Fuzzy Subsets, 1992, Kluwer Academic Publishers (Dordrecht), 68–69.
[20] Point-set lattice-theoretic topology, Fuzzy Sets and Systems40(1991) 297–345.
[21] Functor categories in poslat popology, Abstracts of the Fifth International Congress on Topology (1990) 33–36, Lecce (Italy), 17–21 September 1990, editor C. Guido.
[22] Proceedings of the Eleventh International Seminar on Fuzzy Set Theory, Volume 4(1989) of the Communications of the IFSA Mathematics Chapter, editor.
[23] Generalizations of coherence,Proceedings of the Eleventh International on Fuzzy Set Theory, appeared as Volume 4(1989) of the Communications of the IFSA Mathematics Chapter, 41–44.
[24] Generalizations of sobriety and spatiality,Proceedings of the Eleventh International on Fuzzy Set Theory, appeared as Volume 4(1989) of the Communications of the IFSA Mathematics Chapter, 45–50.
[25] Stone Representation Theorems: an apologetic for fuzzy topology, Proceedings of the Third IFSA World Congress (1989) 262–265.
[26] Categorical aspects of realizations, Proceedings of the Tenth International Seminar on Fuzzy Set Theory 10(1988), Johannes Kepler Universitätsdirektion, Linz (Austria), editors S. Weber and E. P. Klement.
[27] Round Table: Foundations—Categorical Aspects, Realizations, Domains and Ranges of Measures, Proceedings of the Tenth International Seminar on Fuzzy Set Theory 10(1988), Johannes Kepler Universitätsdirektion, Linz (Austria), editors S. Weber and E. P. Klement.
[28] Lowen, para-Lowen, and alpha-level functors and fuzzy topologies on the crisp real line, Journal of Mathematical Analysis and Applications 131(1988) 157–169.
[29] Dynamic topologies and their applications to crisp topologies, fuzzifications of crisp topologies, and fuzzy topologies on the crisp real line, Journal of Mathematical Analysis and Applications 131(1988) 25–66.
[30] A theory of fuzzy uniformities with applications to the fuzzy real lines, Journal of Mathematical Analysis and Applications129(1988) 37–70.
[31] Realizations of events, points of a locale, and the Stone Representation Theorem, Communications of the IFSA Mathematics Chapter 1(1987) 28–33.
[32] A Point-Set Lattice-Theoretic Framework For Topology Which Contains LOC As A Subcategory Of Singelton Spaces And In Which There Are General Classes Of Stone Representation And Compactification Theorems, first printing February 1986, second printing April 1987, Youngstown State University Central Printing Office (Youngstown, Ohio).
[33] Errata, Fuzzy Sets and Systems 20(1986) 107-108.
[34] Complete fuzzy topological hyperfields and fuzzy multiplication in the fuzzy real lines, Fuzzy Sets and Systems 15(1985) 285–310.
[35] Proceedings of the Second Conference on Topology and Fuzzy Sets, May 1985, Youngstown State University, Central Printing Office, 174 pages, editor.
[36] Open questions on dynamic topologies and para-Lowen functors, Proceedings of the Sixth International Seminar on Fuzzy Set Theory6(1984) 151–153, Johannes. Kepler Universitätsdirektion, Linz (Austria), editor E. P. Klement.
[37] Proceedings of the Conference on Fuzzy Sets and Fuzzy Topology, December 1983, Youngstown State University, Central Printing Office, 144 pages, editor.
[38] Separation axioms and the fuzzy real lines, Fuzzy Sets and Systems 11(1983) 163–183.
[39] A categorical accommodation of various notions of fuzzy topology, Fuzzy Sets and Systems 9(1983) 241–265.
[40] Segments in convex metric spaces, Mathematical Chronicle12(1983) 135–138. (joint work with D. H. Pettey of the University of Missouri-Columbia).
[41] Fuzzy addition in the fuzzy real line, Fuzzy Sets and Systems8(1982) 39–52.
[42] The L-fuzzy real line and its subspaces, Fuzzy Set and Possibility Theory: Recent Developments (1982) 402–418, Pergemon Press, Oxford, editor R. R. Yager.
[43] Connectivity and the L-fuzzy unit interval, Rocky Mountain Journal of Mathematics 12(1982) 113–121.
[44] Open questions in fuzzy topology, Proceedings of the Third International Seminar on Fuzzy Set Theory 3(1981) 241–251, Johannes Kepler Universitätsdirektion, Linz (Austria), editor E. P. Klement.
[45] Fuzzy arithmetic and fuzzy topology, Applied Systems and Cybernetics VI(1981) 2803–2807, Pergemon Press, editor G. E. Lasker.
[46] Suitability in fuzzy topological spaces, Journal of Mathematical Analysis and Applications 79(1981) 273–285.
[47] Locally starlike decompositions of separable metric spaces, Fundamenta Mathematicae 112(1981) 61–68.
[48] A lattice of continuities for fuzzy topological spaces, Journal of Mathematical Analysis and Applications 79(1981) 244–255.
[49] The Hausdorff separation axiom for fuzzy topological spaces, Topology and its Applications 11(1980) 319–334.
[50] U.s.c. decompositions of convex metric spaces, Fundamenta Mathematicae 105(1980) 213–227.
[51] Retracts of Tychonov and normal spaces, Fundamenta Mathematicae79(1973) 23–31.