Subgroups of paratopological groups and feebly compact groups

[EN] 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 tha...

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Detalles Bibliográficos
Autores: Fernández, Manuel, Tkachenko, Mikhail G.
Tipo de recurso: artículo
Fecha de publicación:2014
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/43631
Acceso en línea:https://riunet.upv.es/handle/10251/43631
Access Level:acceso abierto
Palabra clave:Feebly compact
Precompact
Paratopological group
Subsemigroup
Topologically periodic
Descripción
Sumario:[EN] 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.