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Sequential topological conditions in โ„ in the absence of the axiom of choice

Sequential topological conditions in โ„ in the absence of the axiom of choice

Abstract It is known that โ€“ assuming the axiom of choice โ€“ for subsets A of โ„ the following hold: (a) A is compact iff it is sequentially compact, (b) A is complete iff it is closed in โ„, (c) โ„ is a sequential space. We will show that these โ€ฆ