5 citations · 14 across the 12 of their papers we have counts for
13 papers · 1 filter
-spaces in the absence of the Axiom of Choice
Kyriakos Keremedis, AliReza Olfati, Eliza Wajch
A -space is a topological space whose every -set is open. In this article, basic properties of -spaces are investigated in the absence of the Axiom of Choice. New weaker…
Countable products and countable sums of compact metrizable spaces in the absence of the Axiom of Choice
Kyriakos Keremedis, Eleftherios Tachtsis, Eliza Wajch
The main aim of the article is to show, in the absence of the Axiom of Choice, relationships between the following, independent of , statements: "Every countable produ…
-spaces, sequential spaces and related topics in the absence of the axiom of choice
Kyriakos Keremedis, Eliza Wajch
In the absence of the axiom of choice, new results concerning sequential, Fréchet-Urysohn, -spaces, very -spaces, Loeb and Cantor completely metrizable spaces are shown. New…
On subcompactness and countable subcompactness of metrizable spaces in ZF
Kyriakos Keremedis
We show in ZF that: (i) Every subcompact metrizable space is completely metrizable, and every completely metrizable space is countably subcompact. (ii) A metrizable space X=(X,T) i…
On iso-dense and scattered spaces in
Kyriakos Keremedis, Eleftherios Tachtsis, Eliza Wajch
A topological space is iso-dense if it has a dense set of isolated points. A topological space is scattered if each of its non-empty subspaces has an isolated point. In $\mathbf{ZF…
Second-countable compact Hausdorff spaces as remainders in and two new notions of infiniteness
Kyriakos Keremedis, Eleftherios Tachtsis, Eliza Wajch
In the absence of the Axiom of Choice, necessary and sufficient conditions for a locally compact Hausdorff space to have all non-empty second-countable compact Hausdorff spaces as…
Several amazing discoveries about compact metrizable spaces in ZF
Kyriakos Keremedis, Eleftherios Tachtsis, Eliza Wajch
In the absence of the axiom of choice, the set-theoretic status of many natural statements about metrizable compact spaces is investigated. Some of the statements are provable in $…
Cuf products and cuf sums of (quasi)-metrizable spaces in
Kyriakos Keremedis, Eliza Wajch
A cuf space (set, resp.) is a space (set, resp.) which is a countable union of finite subspaces (subsets, resp.). It is proved in (with the absence of the axiom of ch…
Denumerable cellular families in Hausdorff spaces and towers of Boolean algebras in
Kyriakos Keremedis, Eliza Wajch
A denumerable cellular family of a topological space is an infinitely countable collection of pairwise disjoint non-empty open sets of . It is proved that…
On Loeb and sequential spaces in
Kyriakos Keremedis, Eliza Wajch
A topological space is called Loeb if the collection of all its non-empty closed sets has a choice function. In this article, in the absence of the axiom of choice, connections bet…
On densely complete metric spaces and extensions of uniformly continuous functions in
Kyriakos Keremedis, Eliza Wajch
A metric space is called densely complete if there exists a dense set in such that every Cauchy sequence of points of converges in .…
Compact complement topologies and k-spaces
Kyriakos Keremedis, Cenap Özel, Artur Piękosz +2
Let be a Hausdorff space, where is an infinite set. The compact complement topology on is defined by: $τ^{\star}=\{\emptyset\} \cup \{X\setminus M, \tex…
Hausdorff compactifications in ZF
Kyriakos Keremedis, Eliza Wajch
For a compactification of a Tychonoff space , the algebra of all functions that are continuously extendable over is denoted by . It is shown that…