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

摘要

A space X is sequentially separable if there is a countable D ? X 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.