S. E. RODABAUGH,
Professor, Youngstown State University
Department of Mathematics and Statistics
Research and Scholarly Work
Works in progress:
[74] Standards for submissions in topology and category theory, in progress,
intended for publication in Fuzzy Sets and Systems (area editor for
Fuzzy Sets and Systems in Topology and Category Theory).
[73] Comparison of localic and fuzzy topological products, in progress.
[72] Concrete categorial adjunctions induced from families of fibre maps,
with C. Ostheimer, in progress.
[71] Necessity of anti-stratified spaces in lattice-valued mathematics, in progress.
[70] Uncountably many families of countably infinitely many adjunctive
powerset theories in SetR with applications to binary multirelations
in programming semantics, being written up.
Works being written up:
[69] A measure-theoretic approach to fuzzy subsethood operators, with V. Dimitrijevic,
Works in submission:
[68] Functorial comparisons of bitopology and topology and the case for
redundancy of bitopology in lattice-valued mathematics, submitted to
Applied General Topology, 37 pages.
[67] Functorial relationships between lattice-valued topology and topological systems,
with J. Denniston, submitted to Quaestiones Mathematicae, in submission, 67 pages.
[66] Category theoretic properties of lattice-valued frames, with A. Pultr, submitted to
Fuzzy Sets and Systems, 66 pages.
Works to appear:
[65] Relationship of algebraic theories to powerset theories and fuzzy topological
theories for lattice-valued mathematics, International Journal of Mathematics and
Mathematical Sciences, to appear, 70 pages (galley proofs).
[64] Relationship of algebraic theories to powersets over objects in Set and
,
S. Gottwald, Petr Hájek, U. Höhle, P. Klement, eds, to appear, 27 pages.
Works published:
[63] Order theoretic, topological, categorical redundancies of interval-valued sets,
grey sets, vague sets, interval-valued "intuitionistic sets, "intuitionistic" fuzzy
sets and topologies, with Javier Gutíerrez-García, Fuzzy Sets and Systems.156(2005),
445–484.
[62] Necessary and sufficient conditions for powersets in Set and
to form
algebraic theories, in S. Gottwald, Petr Hájek, U. Höhle, P. Klement, eds,
Fuzzy Logics and Related Structures: Abstracts, Universitätsdirektion of
Johannes Kepler Universität (Linz, 2005), 89–97.
[61] Transitions to Graduate Mathematics: Order Theoretic Primer in Mathematical
Foundations, present printing by Youngstown State University Bookstore (Kilcawley Center):
10929520, graduate text, in progress. Used in required core graduate course Mathematics 6915
(Mathematical Foundations) since Fall 1992.
[60] Point-set lattice-theoretic (poslat) topology: a (partly) categorical perspective, in E. P. Klement,
E. Papp, eds, Mathematics of Fuzzy Systems: Abstracts, Universitätsdirektion of Johannes Kepler
Universität (Linz, 2004), 181–193.
[59] Topological and Algebraic Structures in Fuzzy Sets: Recent Developments in the Mathematics
of Fuzzy Sets, chief editor, with E. P. Klement, Trends in Logic 20(2003), Kluwer Academic
Publishers (Boston/Dordrecht/London).
[58] Introduction, with E. P. Klement, in [59], 1–16 (this introduction contains original ideas woven
into an extensive contextualization of the chapters of [59] using 117 references).
[57] Lattice-valued frames, functor categories, and classes of sober spaces, with
A. Pultr, Chapter 6 in [59], 153–187.
[56] Weakening the requriement that L be a complete chain, with U. Höhle, appendix to
Chapter 6 in [59], 189–197.
[55] Axiomatic foundations for uniform operator quasi-uniformities, Chapter 7 in [59],
199–233.
[54] Examples for different sobrieties in fixed-basis topology, with A. Pultr, Chapter 17 in [59], 427–440.
[53] Fuzzy topology, Encyclopaedia of Mathematics 13: Supplement III (2002), 168–169,
managing editor M. Hazewinkel, Kluwer Academic Publishers (Boston/Dordrecht/ London).
[52] Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory , editor, with U. Höhle,
Handbooks of Fuzzy Sets 3(1999), Kluwer Academic Publishers (Boston/Dordrecht/London).
[51] Powerset operator foundations for poslat set theories and topologies, in [50], 91–116.
[50] Categorical foundations for variable-basis fuzzy topology, in [50], 273–388.
[49] Separation axioms: representation theorems, compactness, and compactifications, in [50],
[48] Fuzzy real lines and dual real lines as poslat topological, uniform, and metric ordered
semirings with unity, in [50], 607–632.
[47] Topological and Algebraic Structures:: Abstracts of Twentieth Linz Seminar, editor, with E. P.
Klement, Fuzzy Logic Laboratorium Linz (Hagenberg) / Institüt für Algebra, Stochastik, und
Wissenbasierte Mathematische Systeme / Johannes Kepler Universität (Linz) (1999).
[46] Variable basis fuzzy topology and compactifications: a status report, in [47], 34–35.
[45] Covering/Hutton fuzzy uniformities: preliminary remarks, in [47], 52.
[44] Undergraduate mathematics programs overseas: part II: the Basque country, The Art and
Science of Teaching 2:3 (1997), 6–7, College of Arts & Sciences, Youngstown State University.
[43] Undergraduate mathematics programs overseas: part I: South Africa, The Art and
Science of Teaching 2:2 (1997), 6–7, College of Arts & Sciences, Youngstown State University.
[42] Powerset operator based foundation for point-set lattice-theoretic (poslat) set theories
and topologies, Quaestiones Mathematicae 20(3)(1997), 463–530.
[41] Special Issue on Fuzzy Topology, Fuzzy Sets and Systems 73(1995), 1–183, co-editor with
[40] Applications of localic separation axioms, compactness axioms, representations, and
compactifications to poslat topological spaces, in [41], 55–87.
[39] Necessity of Chang-Goguen topologies, Rendiconti Cir. Mat. Palermo (Suppl.)
Series II:29(1992), 299–314.
[38] Applications of Category Theory to Fuzzy Subsets, 1992, chief editor, with E. P. Klement,
U. Höhle, Theory and Decision Library: Series B: Mathematical and Statistical Methods
14(1992), Kluwer Academic Publishers (Boston/Dordrecht/London).
[37] Categorical frameworks for Stone Representation Theories, in [38], 177–232.
[36] Roundtable: model-theoretic vis-a-vis non-model-theoretic fuzzy set theories,
in [38], 59–67.
[35] Roundtable: open questions in logic and topology, in [38], 68–69.
[34] Point-set lattice-theoretic topology, Fuzzy Sets and Systems 40(1991), 297–345.
[33] Functor categories in poslat popology, in C. Guido, ed, Abstracts of the Fifth
International Congress on Topology (Lecce (Italy), 17–21 September 1990), 33–36.
[32] Proceedings of the Eleventh International Seminar on Fuzzy Set Theory, editor,
Communications of the IFSA Mathematics Chapter 4(1989).
[31] Generalizations of coherence, in [31], 41–44.
[30] Generalizations of sobriety and spatiality, in [31], 45–50.
[29] Stone representation theorems: an apologetic for fuzzy topology, Proceedings of the
Third IFSA World Congress (Seattle, 1989), 262–265.
[28] Round Table: Foundations—Categorical Aspects, Realizations, Domains and Ranges
of Measures, in S. Weber and E. P. Klement, eds, Proceedings of the Tenth International
Seminar on Fuzzy Set Theory 10(1988), 80–90, Johannes Kepler Universitätsdirektion,
[27] Categorical aspects of realizations, in [28], 80–87.
[26] 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.
[25] 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.
[24] A theory of fuzzy uniformities with applications to the fuzzy real lines, Journal of
Mathematical Analysis and Applications 129(1988), 37–70.
[23] Subject classifications: Section 2: Mathematical Aspects (applications to pure and
applied mathematics), with U. Höhle, written for Fuzzy Sets and Systems by invitation
of Editorial Board (September 1988), first appeared in D. Dubois, H. Prade, S. Sessa,
Recent literature, Fuzzy Sets and Systems 35(1990), 219–216.
[22] Realizations of events, points of a locale, and the Stone Representation Theorem,
Communications of the IFSA Mathematics Chapter 1(1987), 28–33.
[21] A Point-Set Lattice-Theoretic Framework T 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).
[20] Errata, Fuzzy Sets and Systems 20(1986), 107-108.
[19] Locales are singleton fuzzy topological spaces, in Z. Piotrowski, ed, Proceedings of the
Second Conference on Topology and Fuzzy Sets (Youngstown State University: May 1985,
1986), 7, Youngstown State University Central Printing Office.
[18] Complete fuzzy topological hyperfields and fuzzy multiplication in the fuzzy real lines,
Fuzzy Sets and Systems 15(1985), 285–310.
[17] Open questions on dynamic topologies and para-Lowen functors, Proceedings of the
Sixth International Seminar on Fuzzy Set Theory 6(1984), 151–153, Johannes. Kepler
Universitätsdirektion, Linz (Austria), editor E. P. Klement.
[16] Proceedings of the Conference on Fuzzy Sets and Fuzzy Topology (Youngstown State
University, December 1983), editor, Youngstown State University Central Printing Office,
[15] Separation axioms and the fuzzy real lines, Fuzzy Sets and Systems 11(1983), 163–183.
[14] A categorical accommodation of various notions of fuzzy topology, Fuzzy Sets and Systems
[13] Segments in convex metric spaces, with D. H. Pettey, Math. Chronicle 12(1983), 135–138.
[12] Fuzzy addition in the fuzzy real line, Fuzzy Sets and Systems 8(1982), 39–52.
[11] The L-fuzzy real line and its subspaces, in R. R. Yager, ed, Fuzzy Set and Possibility Theory:
Recent Developments (1982), 402–418, Pergemon Press (Oxford).
[10] Connectivity and the L-fuzzy unit interval, Rocky Mountain Journal of Mathematics 12(1982),
[9] A categorical accommodation of various notions of fuzzy topology: preliminary report, in
E. P. Klement, ed, Proceedings of the Third International Seminar on Fuzzy Set Theory 3(1981),
119–152, Johannes Kepler Universitätsdirektion, Linz (Austria).
[8] Open questions in fuzzy topology, in E. P. Klement, ed, Proceedings of the Third International
Seminar on Fuzzy Set Theory 3(1981), 241–251, Johannes Kepler Universitätsdirektion,
[7] Fuzzy arithmetic and fuzzy topology, in G. E. Lasker, Applied Systems and Cybernetics VI(1981),
2803–2807, Pergemon Press (Oxford).
[6] Suitability in fuzzy topological spaces, Journal of Mathematical Analysis and Applications
[5] Locally starlike decompositions of separable metric spaces, Fundamenta Mathematicae
[4] A lattice of continuities for fuzzy topological spaces, Journal of Mathematical Analysis
and Applications 79(1981), 244–255.
[3] The Hausdorff separation axiom for fuzzy topological spaces, Topology and Its Applications
[2] U.s.c. decompositions of convex metric spaces, Fundamenta Mathematicae 105(1980), 213–227.
[1] Retracts of Tychonov and normal spaces, Fundamenta Mathematicae 79(1973), 23–31.