# $k$-spaces, sequential spaces and related topics in the absence of the axiom of choice

@inproceedings{Keremedis2021kspacesSS, title={\$k\$-spaces, sequential spaces and related topics in the absence of the axiom of choice}, author={Kyriakos Keremedis and Eliza Wajch}, year={2021} }

In the absence of the axiom of choice, new results concerning sequential, Fréchet-Urysohn, k-spaces, very k-spaces, Loeb and Cantor completely metrizable spaces are shown. New choice principles are introduced. Among many other theorems, it is proved in ZF that every Loeb, T3-space having a base expressible as a countable union of finite sets is a metrizable second-countable space whose every Fσ-subspace is separable; moreover, every Gδ-subspace of a second-countable, Cantor completely…

## One Citation

Partition models, Permutations of infinite sets without fixed points, Variants of CAC, and weak forms of AC

- Mathematics
- 2021

We study new relations of the following statements with weak choice principles in ZF (ZermeloFraenkel set theory without the Axiom of Choice (AC)) and ZFA (ZF with the axiom of extensionality…

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