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.
@article{bwmeta1.element.doi-10_2478_s11533-012-0140-5,
author = {Angelo Bella and Maddalena Bonanzinga and Mikhail Matveev},
title = {Sequential + separable vs sequentially separable and another variation on selective separability},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {530-538},
zbl = {1264.54045},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0140-5}
}
Angelo Bella; Maddalena Bonanzinga; Mikhail Matveev. Sequential + separable vs sequentially separable and another variation on selective separability. Open Mathematics, Tome 11 (2013) pp. 530-538. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0140-5/
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