, Volume 11, Issue 3, pp 530-538
Date: 16 Nov 2012

Sequential + separable vs sequentially separable and another variation on selective separability

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Abstract

A space X is sequentially separable if there is a countable DX such that every point of X is the limit of a sequence of points from D. Neither “sequential + separable” nor “sequentially separable” implies the other. Some examples of this are presented and some conditions under which one of the two implies the other are discussed. A selective version of sequential separability is also considered.