On the Novak number of a hyperspace
An estimate for the Novak number of a hyperspace with the Vietoris topology is given. As a consequence it is shown that this cardinal function can decrease passing from a space to its hyperspace.
On the preservation of separation axioms in products
We give sufficient and necessary conditions to be fulfilled by a filter and an ideal in order that the -quotient space of the -ideal product space preserves -properties () (“in the sense of the Łos theorem”). Tychonoff products, box products and ultraproducts appear as special cases of the general construction.
On the product of a perfect paracompact space and a countable product of scattered paracompact spaces
On the product of separable metric spaces.
On the product topology associated with semi-closed sets
On the Productivity of l_1(Γ) Embeddings
On the pullback stability of a quotient map with respect to a closure operator.
On the quantification of uniform properties
Approach spaces ([4], [5]) turned out to be a natural setting for the quantification of topological properties. Thus a measure of compactness for approach spaces generalizing the well-known Kuratowski measure of non-compactness for metric spaces was defined ([3]). This article shows that approach uniformities (introduced in [6]) have the same advantage with respect to uniform concepts: they allow a nice quantification of uniform properties, such as total boundedness and completeness.
On the set function
Inspired by the work that Professor Janusz R. Prajs did on homogeneous metric continua in his paper (2010) and the version of his work for Hausdorff continua with the uniform property of Effros done by this author, we introduce a new set function, , and present properties of it.
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 simplicity of some categories of closure spaces
On the singularity of Mazurkiewicz in absolute neighborhood retracts
On the strong local simple connectivity of the decomposition spaces of toroidal decompositions
On The Sup And Inf Invariance Of Some Separation Axioms
On the sup and inf invariance of some seperation axioms.
On the uniform paracompactness of the product of two uniform spaces
On topological factors of 3 dimensional locally connected continuum embeddable in
On totally bounded games
On two theorems of Dyer
On uniform connection properties