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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…
On Urysohn's Lemma for generalized topological spaces in ZF
Jacek Hejduk, Eliza Wajch
A strong generalized topological space is an ordered pair such that is a set and is a collection of subsets of such…
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 $…