6 papers
On -Frechet-Urysohn topological groups
Saak Gabriyelyan, Alexander V. Osipov, Evgenii Reznichenko
We characterize -Fréchet--Urysohn topological groups. Using this characterization we show that: (1) a hemicompact topological group is -Fréchet--Urysohn iff it is locally…
Baire-type properties of topological vector spaces
Saak Gabriyelyan, Alexander V. Osipov, Evgenii Reznichenko
Burzyk, KliÅ and Lipecki proved that every topological vector space (tvs) with the property is a Baire space. Kcakol and Sánchez Ruiz proved that every sequentially com…
Completeness and reflexivity type properties of
Saak Gabriyelyan, Alexander V. Osipov, Evgenii Reznichenko
For a Tychonoff space , denotes the space of all Baire-one functions on endowed with the pointwise topology. We prove that the following assertions are equivalent:…
New classes of compact-type spaces
Saak Gabriyelyan, Evgenii Reznichenko
Being motivated by the notions of -Fréchet--Urysohn spaces and -spaces introduced by Arhangel'skii, the notion of sequential spaces and the study of Ascoli spaces, we intr…
-spaces
Saak Gabriyelyan, Evgenii Reznichenko
We say that a Tychonoff space is a -space if it is homeomorphic to a closed subspace of for some locally compact space . The class of -spaces is strictly be…
Functions on products with applications to Ascoli spaces, -spaces and -spaces
Saak Gabriyelyan, Evgenii Reznichenko
We prove that a Tychonoff space is (sequentially) Ascoli iff for every compact space (resp., for a convergent sequence ), each separately continuous -continu…