# A note on pseudobounded paratopological groups

Fucai Lin; Shou Lin; Iván Sánchez

Topological Algebra and its Applications (2014)

- Volume: 2, Issue: 1, page 11-18, electronic only
- ISSN: 2299-3231

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topFucai Lin, Shou Lin, and Iván Sánchez. "A note on pseudobounded paratopological groups." Topological Algebra and its Applications 2.1 (2014): 11-18, electronic only. <http://eudml.org/doc/267456>.

@article{FucaiLin2014,

abstract = {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.},

author = {Fucai Lin, Shou Lin, Iván Sánchez},

journal = {Topological Algebra and its Applications},

keywords = {Paratopological group; Pseudobounded; ω-pseudobounded; Topological group; Premeager space; Lusin space; paratopological group; pseudobounded; -pseudobounded; topological group; premeager space},

language = {eng},

number = {1},

pages = {11-18, electronic only},

title = {A note on pseudobounded paratopological groups},

url = {http://eudml.org/doc/267456},

volume = {2},

year = {2014},

}

TY - JOUR

AU - Fucai Lin

AU - Shou Lin

AU - Iván Sánchez

TI - A note on pseudobounded paratopological groups

JO - Topological Algebra and its Applications

PY - 2014

VL - 2

IS - 1

SP - 11

EP - 18, electronic only

AB - 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.

LA - eng

KW - Paratopological group; Pseudobounded; ω-pseudobounded; Topological group; Premeager space; Lusin space; paratopological group; pseudobounded; -pseudobounded; topological group; premeager space

UR - http://eudml.org/doc/267456

ER -

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