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Different versions of a first countable space without choice |
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| Authors: | Kyriakos Keremedis Eleftherios Tachtsis |
| Institution: | a Department of Mathematics, University of the Aegean, Karlovassi 83200, Samos, Greece b Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, Karlovassi 83200, Samos, Greece |
| Abstract: | We show that two versions of a first countable topological space which are equivalent in ZFC set theory split in the absence of the Axiom of Choice AC. This answers in the negative a related question from Gutierres “What is a first countable space?”. |
| Keywords: | 03E25 03E35 54D70 |
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