We prove the following statements: (1) every Tychonoff linked-Lindelöf (centered-Lindelöf, star countable) space can be represented as a closed subspace in a Tychonoff pseudocompact absolutely star countable space; (2) every Hausdorff (regular, Tychonoff) linked-Lindelöf space can be represented as a closed G δ-subspace in a Hausdorff (regular, Tychonoff) absolutely star countable space; (3) there exists a pseudocompact absolutely star countable Tychonoff space having a regular closed subspace which is not star countable (hence not absolutely star countable); (4) assuming , there exists an absolutely star countable normal space having a regular closed subspace which is not star countable (hence not absolutely star countable).
@article{bwmeta1.element.doi-10_2478_s11533-013-0276-y,
author = {Yan-Kui Song},
title = {Remarks on absolutely star countable spaces},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {1755-1762},
zbl = {1284.54038},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0276-y}
}
Yan-Kui Song. Remarks on absolutely star countable spaces. Open Mathematics, Tome 11 (2013) pp. 1755-1762. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0276-y/
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