Subgroups of paratopological groups and feebly compact groups
Keywords:feebly compact, precompact, paratopological group, subsemigroup, topologically periodic
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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