Subgroups of paratopological groups and feebly compact groups

• Fernández, Manuel ^[1] ; Tkachenko, Mikhail G. ^[2]
  1. [1] Universidad Autónoma de la Ciudad de México

     Universidad Autónoma de la Ciudad de México

     México

     
  2. [2] Universidad Autónoma Metropolitana

     Universidad Autónoma Metropolitana

     México

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 15, Nº. 2, 2014, págs. 235-248
• Idioma: inglés
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• Resumen

  • 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.