A note on pseudobounded paratopological groups

• Autorzy: Fucai Lin , Shou Lin , Iván Sánchez
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Paratopological group; Pseudobounded; ω-pseudobounded; Topological group; Premeager space; Lusin space

Kategorie tematyczne

• 54C05: Continuous maps
• 54A05: Topological spaces and generalizations (closure spaces, etc.)
• 54H11: Topological groups
• 54B05: Subspaces

• Wydawca: De Gruyter Open
• Czasopismo: Topological Algebra and its Applications
• Rocznik: 2014
• Tom: 2
• Numer: 1

Daty

otrzymano

2013-11-30

zaakceptowano

2014-02-01

online

2014-06-27

Twórcy

autor

Fucai Lin

• School of mathematics and statistics, Minnan Normal University, Zhangzhou 363000, P. R. China

autor

Shou Lin

• Institute of Mathematics, Ningde Teachers’ College, Ningde, Fujian 352100, P. R. China

autor

Iván Sánchez

• Departamento de Matemáticas, Universidad Autónoma Metropolitana, Av. San Rafael
  Atlixco 186, Col. Vicentina, Del. Iztapalapa, C.P. 09340, Mexico, D.F.

Bibliografia

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Identyfikatory

DOI

10.2478/taa-2014-0003