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

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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.
  • Dipartimento di Matematica, Cittá Universitaria, Viale A. Doria 6, 98125, Catania, Italy
  • Dipartimento di Matematica, Università di Messina, Viale F. Stagno d’Alcontres 31, 98166, Messina, Italy
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