Let G be a paratopological group. Then G is said to be pseudobounded (resp. ω-pseudobounded) if for every neighbourhood V of the identity e in G, there exists a natural number n such that G = Vn (resp.we have G = ∪ n∈N Vn). We show that every feebly compact (2-pseudocompact) pseudobounded (ω-pseudobounded) premeager paratopological group is a topological group. Also,we prove that if G is a totally ω-pseudobounded paratopological group such that G is a Lusin space, then is G a topological group. We present some examples of paratopological groups with interesting properties: (1) There exists a metrizable, zero-dimensional and pseudobounded topological group; (2) There exists a Hausdorff ω-pseudobounded paratopological group G such that G contains a dense subgroup which is not ω-pseudobounded; (3) There exists a Hausdorff connected paratopological group which is not ω-pseudobounded.
@article{bwmeta1.element.doi-10_2478_taa-2014-0003,
author = {Fucai Lin and Shou Lin and Iv\'an S\'anchez},
title = {A note on pseudobounded paratopological groups},
journal = {Topological Algebra and its Applications},
volume = {2},
year = {2014},
zbl = {1311.54025},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_taa-2014-0003}
}
Fucai Lin; Shou Lin; Iván Sánchez. A note on pseudobounded paratopological groups. Topological Algebra and its Applications, Tome 2 (2014) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_taa-2014-0003/
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