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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