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A note on pseudobounded paratopological groups

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Lin F., Lin S., Sánchez I.

Topological Algebra and its Applications

2014

tom 2

nr 1

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.

Ograniczanie wyników

1 Topological Algebra and its Applications

1 Lin F.

1 Lin S.

1 Sánchez I.

1 2014

Wyniki wyszukiwania

A note on pseudobounded paratopological groups