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On dense subspaces satisfying stronger separation axioms

Ofelia Teresa Alas, Mihail G. Tkachenko, Vladimir Vladimirovich Tkachuk, Richard Gordon Wilson, Ivan V. Yashchenko (2001)

Czechoslovak Mathematical Journal

We prove that it is independent of ZFC whether every Hausdorff countable space of weight less than c has a dense regular subspace. Examples are given of countable Hausdorff spaces of weight c which do not have dense Urysohn subspaces. We also construct an example of a countable Urysohn space, which has no dense completely Hausdorff subspace. On the other hand, we establish that every Hausdorff space of π -weight less than 𝔭 has a dense completely Hausdorff (and hence Urysohn) subspace. We show that...

On finest unitary extensions of topological monoids

Boris G. Averbukh (2015)

Topological Algebra and its Applications

We prove that the Wyler completion of the unitary Cauchy space on a given Hausdorff topological 5 monoid consisting of the underlying set of this monoid and of the family of unitary Cauchy filters on it, is a T2-topological space and, in the commutative case, an abstract monoid containing the initial one.

On hereditarily normal topological groups

(2012)

Fundamenta Mathematicae

We investigate hereditarily normal topological groups and their subspaces. We prove that every compact subspace of a hereditarily normal topological group is metrizable. To prove this statement we first show that a hereditarily normal topological group with a non-trivial convergent sequence has G δ -diagonal. This implies, in particular, that every countably compact subspace of a hereditarily normal topological group with a non-trivial convergent sequence is metrizable. Another corollary is that under...

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