On sequentially closed subsets of the real line in

Mathematical Logic Quarterly 61 (1-2):24-31 (2015)
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Abstract

We show: iff every countable product of sequential metric spaces (sequentially closed subsets are closed) is a sequential metric space iff every complete metric space is Cantor complete. Every infinite subset X of has a countably infinite subset iff every infinite sequentially closed subset of includes an infinite closed subset. The statement “ is sequential” is equivalent to each one of the following propositions: Every sequentially closed subset A of includes a countable cofinal subset C, for every sequentially closed subset A of, is a meager subset of, for every sequentially closed subset A of,, every sequentially closed subset of is separable, every sequentially closed subset of is Cantor complete, every complete subspace of is Cantor complete.

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10.1002/malq.201300008

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Citations of this work

Sequential topologies and Dedekind finite sets.Jindřich Zapletal - 2022 - Mathematical Logic Quarterly 68 (1):107-109.

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References found in this work

Non-constructive Properties of the Real Numbers.J. E. Rubin, K. Keremedis & Paul Howard - 2001 - Mathematical Logic Quarterly 47 (3):423-431.
On countable choice and sequential spaces.Gonçalo Gutierres - 2008 - Mathematical Logic Quarterly 54 (2):145-152.

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