A 3-dimensional absolute retract which does not contain any disk
A 3-dimensional irreducible compact absolute retract which contains no disc
A Banach fixed point theorem for topolocical spaces
A basic approach to the perfect extensions of spaces
In this paper we generalize the notion of perfect compactification of a Tychonoff space to a generic extension of any space by introducing the concept of perfect pair. This allow us to simplify the treatment in a basic way and in a more general setting. Some [S], [S], and [D]’s results are improved and new characterizations for perfect (Hausdorff) extensions of spaces are obtained.
A Basic Fixed Point Theorem
The paper contains a fixed point theorem for stable mappings in metric discus spaces (Theorem 10). A consequence is Theorem 11 which is a far-reaching extension of the fundamental result of Browder, Göhde and Kirk for non-expansive mappings.
A Bing-Borsuk retract which contains a 2-dimensional absolute retract [Book]
A Boolean view of sequential compactness
A bornological approach to rotundity and smoothness applied to approximation.
A boundary set for the Hilbert cube containing no arcs
A -continuum is metrizable if and only if it admits a Whitney map for .
A Cantor set in the plane that is not σ-monotone
A metric space (X,d) is monotone if there is a linear order < on X and a constant c such that d(x,y) ≤ cd(x,z) for all x < y < z in X, and σ-monotone if it is a countable union of monotone subspaces. A planar set homeomorphic to the Cantor set that is not σ-monotone is constructed and investigated. It follows that there is a metric on a Cantor set that is not σ-monotone. This answers a question raised by the second author.
A categorical account of the localic closed subgroup theorem
Given an axiomatic account of the category of locales the closed subgroup theorem is proved. The theorem is seen as a consequence of a categorical account of the Hofmann-Mislove theorem. The categorical account has an order dual providing a new result for locale theory: every compact subgroup is necessarily fitted.
A categorical concept of completion of objects
We introduce the concept of firm classes of morphisms as basis for the axiomatic study of completions of objects in arbitrary categories. Results on objects injective with respect to given morphism classes are included. In a finitely well-complete category, firm classes are precisely the coessential first factors of morphism factorization structures.
A categorical generalization of completely Hausdorff spaces
A categorical guide to separation, compactness and perfectness.
A categorical proof of the equivalence of local compactness and exponentiability in locale theory
A category analogue of the density topology
A category Ψ-density topology
Ψ-density point of a Lebesgue measurable set was introduced by Taylor in [Taylor S.J., On strengthening the Lebesgue Density Theorem, Fund. Math., 1958, 46, 305–315] and [Taylor S.J., An alternative form of Egoroff’s theorem, Fund. Math., 1960, 48, 169–174] as an answer to a problem posed by Ulam. We present a category analogue of the notion and of the Ψ-density topology. We define a category analogue of the Ψ-density point of the set A at a point x as the Ψ-density point at x of the regular open...
A Čech function in ZFC
A nontrivial surjective Čech closure function is constructed in ZFC.
A Cech-Hurewicz Isomorphism Theorem for Movable Metric Compacta.