• 200? "Not every co-existential map is confluent" (submitted)

• 200? "A syntactically-specified family of topological covering properties
  preserved by co-existential maps and inverse limits" (submitted)

• 200? "On the first-order expressibility of lattice properties related to unicoherence in continua" (submitted)

• 200? "Categoricity and topological graphs" (submitted)

• 200? "Categorical compact Hausdorff spaces" (submitted)

Main Publications:

• 200? "Dendrites, topological graphs, and 2-dominance" Houston Journal of Mathematics (to appear)

• 2006 (with T. Banakh, B. Raines and W. Ruitenburg) "Chainability and Hemmingsen's theorem" Topology and its Applications, vol. 153, no. 14, 2462-2468.

• 2006 "The Chang-Los-Suszko theorem in a topological setting" Archive for Mathematical Logic, vol. 45, no. 1, 97-112.

• 2005 "Mapping properties of co-existentially closed continua" Houston Journal of Mathematics, vol. 31, no. 4, 1047-1063.

• 2003 "Modeling nonintersective adjectives using operator logics" The Review of Modern Logic, vol. 9, nos. 1&2, 9-28.

• 2003 "A survey of ultraproduct constructions in general topology," Topology Atlas Invited Contributions, vol. 8, no. 2, 1-32.

• 2000 "Continua and the co-elementary hierarchy of maps," Topology Proceedings, vol. 25, 45-62.

• 2000 "Some applications of the ultrapower theorem to the theory of compacta," Applied Categorical Structures, vol. 8, 45-66. (See also Topology Atlas.)

• 1999 "A hierarchy of maps between compacta," J. Symbolic Logic, vol. 64, 1628-1644. (See also Topology Atlas.)

• 1997 "Co-elementary equivalence, co-elementary maps, and generalized arcs," Proc. Amer. Math. Soc., vol. 125, 3715-3720. (See also Topology Atlas.)

• 1994 "Topologies invariant under a group action," J. Pure and Applied Algebra, vol. 97, 221-245.

• 1994 "Topological measures of systems of sets," in "Papers on General Topology and Applications" (Queens College, NY, 1992), Ann. New York Acad. Sci., vol. 728, 1-15.

• 1993 "H-enrichments and their homeomorphism groups, II," in "Papers on General Topology and Applications" (University of Wisconsin-Madison, 1991), Ann. New York Acad. Sci., vol. 704, 6-19.

• 1993 "Pseudobases in direct powers of an algebra," Trans. Amer. Math. Soc., vol. 335, 79-90.

• 1992 "H-enrichments and their homeomorphism groups," Quarterly J. Math., Oxford (2), vol. 43, 127-148.

• 1992 "Minimal freeness and commutativity," Algebra Universalis, vol. 29, 88-108.

• 1991 (w. R.A. McCoy) "H-enrichments of topologies," Topology and Applications, vol. 42, 37-55.

• 1990 (w. W. Ruitenburg) "Notions of relative ubiquity for invariant sets of relational structures," J. Symbolic Logic, vol. 55, 948-986.

• 1990 "Co-elementary equivalence for compact Hausdorff spaces and compact abelian groups," J. Pure and Appled Algebra, vol. 68, 11-26.

• 1990 (w. R.A. McCoy) "On the classification of minimally free rings of continuous functions," in "General Topology and Applications" (Proc. of the 1988 Northeast Conf., R.M. Shortt, ed.) Marcel Dekker, NY, 51-58.

• 1990 "Taxonomies of model-theoretically defined topological properties," J. Symbolic Logic, vol. 55, 589-603.

• 1989 "A note on large minimally free algebras," Algebra Universalis, vol. 26, 346-350.

• 1988 "Model-theoretic characterizations of arcs and simple closed curves," Proc. Amer. Math. Soc., vol. 104, 898-904.

• 1987 "Reduced coproducts of compact Hausdorff spaces," J. Symbolic Logic, vol. 52, 404-424.

• 1985 (w. R. Schutt) "On minimally free algebras," Canadian J. Math., vol. 17, 963-978.

• 1985 (w. R. Fox) "Topological partitions of euclidean space by spheres," Amer. Math. Monthly, vol. 92, 423-424.

• 1984 "First order representations of compact Hausdorff spaces," in "Categorical Topology" (Proc. of the Intl. Conf., Univ. of Toledo, Toledo, OH, H. L. Bentley, et al, eds.) Heldermann Verlag, Berlin, pp. 23-28.

• 1984 "Expressive power in first order topology," J. Symbolic Logic, vol. 49, 478-487.

• 1983 "Topological extensions and subspaces of $\eta_\alpha$-sets," Fundamenta Mathematicae, vol. 118, 191-199.

• 1983 "Obstacles to duality between classes of relational structures," Algebra Universalis, vol. 17, 87-91.

• 1983 (w. R. Fox) "On categories of algebras equivalent to a quasivariety," Algebra Universalis, vol. 16, 153-158.

• 1983 "Coarse topologies in nonstandard extensions via separative ultrafilters," Illinois J. Math., vol. 27, 459-466.

• 1983 "On partitions of plane sets into simple closed curves II," Proc. Amer. Math. Soc., vol. 89, 498-502.

• 1983 "On partitions of plane sets into simple closed curves," Proc. Amer. Math. Soc., vol. 88, 691-698.

• 1983 "On productive classes of function rings," Proc. Amer. Math. Soc., vol. 87, 11-14.

• 1982 "Some obstacles to duality in topological algebra," Canadian J. Math., vol. 34, 80-90.

• 1979 "The total negation of a topological property," Illinois J. Math., vol. 23, 241-252.

• 1979 (w. R. McGovern) "Topological partitions," General Topology and Applications, vol. 10, 215-229.

• 1979 "Topological reduced products via good ultrafilters," General Topology and Applications, vol. 10, 121-137.

• 1977 "Ultraproducts in topology," General Topology and Applications, vol. 7, 283-308.

• 1976 "Topological reduced products and the GCH," Topology Proc., vol. 1, 261-267.

• 1976 "Clopen sets in hyperspaces," Proc. Amer. Math. Soc., vol. 54, 298-302.

Codicils and Notes:

• 1996 "Nonstandard topology," Topology Atlas Invited Contributions, vol. 1, no. 4, 42.

• 1985 "Corrigendum to 'Some obstacles to duality in topological algebra'," Canadian J. Math., vol. 37, 82-83.

• 1984 "Addendum to 'On partitions of plane sets into simple closed curves II'," Proc. Amer. Math. Soc., vol. 91, 658.

• 1979 "Note on 'Ultraproducts in topology'," General Topology and Applications, vol. 10, 231-232.