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

Angelo Bella; Maddalena Bonanzinga; Mikhail Matveev

Open Mathematics (2013)

  • Volume: 11, Issue: 3, page 530-538
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Angelo Bella, Maddalena Bonanzinga, and Mikhail Matveev. "Sequential + separable vs sequentially separable and another variation on selective separability." Open Mathematics 11.3 (2013): 530-538. <http://eudml.org/doc/269246>.

@article{AngeloBella2013,
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.},
author = {Angelo Bella, Maddalena Bonanzinga, Mikhail Matveev},
journal = {Open Mathematics},
keywords = {Sequential space; Separable space; Sequentially separable space; Strongly sequentially separable space; Selective separability; sequential space; separable space; sequentially separable space; strongly sequentially separable space; selective separability},
language = {eng},
number = {3},
pages = {530-538},
title = {Sequential + separable vs sequentially separable and another variation on selective separability},
url = {http://eudml.org/doc/269246},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Angelo Bella
AU - Maddalena Bonanzinga
AU - Mikhail Matveev
TI - Sequential + separable vs sequentially separable and another variation on selective separability
JO - Open Mathematics
PY - 2013
VL - 11
IS - 3
SP - 530
EP - 538
AB - 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.
LA - eng
KW - Sequential space; Separable space; Sequentially separable space; Strongly sequentially separable space; Selective separability; sequential space; separable space; sequentially separable space; strongly sequentially separable space; selective separability
UR - http://eudml.org/doc/269246
ER -

References

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