We show that a regular totally ω-narrow paratopological group G has countable index of regularity, i.e., for every neighborhood U of the identity e of G, we can find a neighborhood V of e and a countable family of neighborhoods of e in G such that ∩W∈γ VW−1⊆ U. We prove that every regular (Hausdorff) totally !-narrow paratopological group is completely regular (functionally Hausdorff). We show that the index of regularity of a regular paratopological group is less than or equal to the weak Lindelöf number. We also prove that every Hausdorff paratopological group with countable π- character has a regular Gσ-diagonal.
@article{bwmeta1.element.doi-10_2478_taa-2013-0005,
author = {Iv\'an S\'anchez},
title = {Cardinal invariants of paratopological groups},
journal = {Topological Algebra and its Applications},
volume = {1},
year = {2013},
pages = {37-45},
zbl = {1296.54043},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_taa-2013-0005}
}
Iván Sánchez. Cardinal invariants of paratopological groups. Topological Algebra and its Applications, Tome 1 (2013) pp. 37-45. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_taa-2013-0005/
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