Sequential topological conditions in ℝ in the absence of the axiom of choice

Mathematical Logic Quarterly 49 (3):293-298 (2003)
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Abstract

It is known that – assuming the axiom of choice – for subsets A of ℝ the following hold: (a) A is compact iff it is sequentially compact, (b) A is complete iff it is closed in ℝ, (c) ℝ is a sequential space. We will show that these assertions are not provable in the absence of the axiom of choice, and that they are equivalent to each.

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10.1002/malq.200310029

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Citations of this work

On countable choice and sequential spaces.Gonçalo Gutierres - 2008 - Mathematical Logic Quarterly 54 (2):145-152.
On sequentially closed subsets of the real line in.Kyriakos Keremedis - 2015 - Mathematical Logic Quarterly 61 (1-2):24-31.
Sequential topologies and Dedekind finite sets.Jindřich Zapletal - 2022 - Mathematical Logic Quarterly 68 (1):107-109.

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