Products of bounded subsets of paratopological groups

Sánchez, Iván; Tkachenko, Mikhail

doi:10.1016/j.topol.2015.03.017

Cited by 14 publications

(1 citation statement)

References 24 publications

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“…This fact is applied in the forthcoming article [15] to show that if B i is a bounded subset of a paratopological group G i , where i ∈ I, then the set i∈I B i is bounded in i∈I G i provided that each group G i is totally ω-narrow or precompact. Again, we impose no separation restrictions on the factors G i 's.…”

Section: Introductionmentioning

confidence: 99%

Applications of the reflection functors in paratopological groups

Tkachenko

2015

Topology and its Applications

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We apply T i -reflections for i = 0, 1, 2, 3, as well as the regular reflection defined by the author in [20] for the further study of paratopological and semitopological groups. We show that many topological properties are invariant and/or inverse invariant under taking T i -reflections in paratopological groups. Using this technique, we prove that every σ-compact paratopological group has the Knaster property and, hence, is of countable cellularity. We also prove that an arbitrary product of locally feebly compact paratopological groups is a Moscow space, thus generalizing a similar fact established earlier for products of feebly compact topological groups. The proof of the latter result is based on the fact that the functor T 2 of Hausdorff reflection 'commutes' with arbitrary products of semitopological groups. In fact, we show that the functors T 0 and T 1 also commute with products of semitopological groups, while the functors T 3 and Reg commute with products of paratopological groups.

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Section: Introductionmentioning

confidence: 99%