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Some Baire category properties of topological groups
Taras Banakh, Olena Hryniv
We present several known and new results on the Baire category properties in topological groups. In particular, we prove that a Baire topological group is metrizable if and onl…
A parallel metrization theorem
Taras Banakh, Olena Hryniv
Two non-empty sets of a metric space are called parallel if for any points and . Answering a question posed on Mathoverflow, w…
The connected countable spaces of Bing and Ritter are topologically homogeneous
Iryna Banakh, Taras Banakh, Olena Hryniv +1
Answering a problem posed by the second author on Mathoverflow, we prove that the connected countable Hausdorff spaces constructed by Bing and Ritter are topologically homogeneous.
Pontryagin duality between compact and discrete abelian inverse monoids
Taras Banakh, Olena Hryniv
For a topological monoid S the dual inverse monoid is the topological monoid of all identity preserving homomorphisms from S to the circle with attached zero. A topological monoid…
Free topological universal algebras and absolute neighborhood retracts
Taras Banakh, Olena Hryniv
We prove that for a complete quasivariety of topological -algebras of countable discrete signature and each submetrizable -space its free topological -a…
Free topological inverse semigroups as infinite-dimensional manifolds
T. Banakh, O. Hryniv
Let be a complete quasivariety of topological inverse Clifford semigroups, containing all topological semilattices. It is shown that the free topological inverse semigroup $F(X…