5 citations · 13 across the 10 of their papers we have counts for
12 papers
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 $…