2012•Open MathematicsOpen access

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

Angelo Bella, Maddalena Bonanzinga, Mikhail Matveev

Abstract

Abstract 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.

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Key concepts: Separable space, Mathematics, Countable set, Sequence (biology), Limit point, Limit (mathematics), Point (geometry), Combinatorics