Subgroups of paratopological groups and feebly compact groups

Authors

  • Manuel Fernández Universidad Autónoma de la Ciudad de México
  • Mikhail Tkachenko Universidad Autónoma Metropolitana

DOI:

https://doi.org/10.4995/agt.2014.3157

Keywords:

feebly compact, precompact, paratopological group, subsemigroup, topologically periodic

Abstract

It is shown that if all countable subgroups of a semitopological group G are precompact, then G is also precompact and that the closure of an arbitrary subgroup of G is again a subgroup. We present a general method of refining the topology of a given commutative paratopological group G such that the group G with the finer topology, say, σ is again a paratopological group containing a subgroup whose closure in (G, σ) is not a subgroup.

It is also proved that a feebly compact paratopological group H is perfectly k-normal and that every Gδ-dense subspace of H is feebly compact.

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References

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Published

2014-07-21

How to Cite

[1]
M. Fernández and M. Tkachenko, “Subgroups of paratopological groups and feebly compact groups”, Appl. Gen. Topol., vol. 15, no. 2, pp. 235–248, Jul. 2014.

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