On the separation properties of
On the set-theoretic strength of the n-compactness of generalized Cantor cubes
We investigate, in set theory without the Axiom of Choice , the set-theoretic strength of the statement Q(n): For every infinite set X, the Tychonoff product , where 2 = 0,1 has the discrete topology, is n-compact, where n = 2,3,4,5 (definitions are given in Section 1). We establish the following results: (1) For n = 3,4,5, Q(n) is, in (Zermelo-Fraenkel set theory minus ), equivalent to the Boolean Prime Ideal Theorem , whereas (2) Q(2) is strictly weaker than in set theory (Zermelo-Fraenkel set...
On the shape of 0-dimensional paracompacta
On the simplicity of some categories of closure spaces
On the subsets of non locally compact points of ultracomplete spaces
In 1998, S. Romaguera [13] introduced the notion of cofinally Čech-complete spaces equivalent to spaces which we later called ultracomplete spaces. We define the subset of points of a space at which is not locally compact and call it an nlc set. In 1999, Garc’ıa-Máynez and S. Romaguera [6] proved that every cofinally Čech-complete space has a bounded nlc set. In 2001, D. Buhagiar [1] proved that every ultracomplete GO-space has a compact nlc set. In this paper, ultracomplete spaces which have...
On The Sup And Inf Invariance Of Some Separation Axioms
On the sup and inf invariance of some seperation axioms.
On the surjective span and semispan of connected metric spaces
On the topological extensions
On the two natural products in a Stone-Cech compactification .
On the uniform paracompactness
On the uniform paracompactness of the product of two uniform spaces
On the weight of nowhere dense subsets in compact spaces.
On the Whitehead theorem in shape theory I
On the ΄΄Fragmentation΄΄ of Certain Pseydocompact Groups
On thick spaces
On tightness in chain-net spaces
On topological ergodic measure spaces.
On topologies generating the Effros Borel structure and on the Effros measurability of the boundary operation
On topologies of free groups