5 papers
Baire property of spaces of -valued continuous functions
Alexander V. Osipov, Evgenii G. Pytkeev
A topological space is Baire if the intersection of any sequence of open dense subsets of is dense in . Let denote the space of all continuous -val…
Every metric space of weight admits a condensation onto a Banach space
Alexander V. Osipov, Evgenii G. Pytkeev
In this paper, we have proved that for each cardinal number such that a metric space of weight admits a bijective continuous mapping onto a Banach space of…
Compact condensations of Hausdorff spaces
Vitalii I. Belugin, Alexander V. Osipov, Evgenii G. Pytkeev
In this paper, we continue to study one of the classic problems in general topology raised by P.S. Alexandrov: when a Hausdorff space has a continuous bijection (a condensation…
On some properties of the space of upper semicontinuous functions
Alexander V. Osipov, Evgenii G. Pytkeev
For a Tychonoff space , we will denote by () a set of all real-valued upper semicontinuous functions (a set of all Baire functions of class 1) defined on $X…
On sequential separability of functional spaces
Alexander V. Osipov, Evgenii G. Pytkeev
In this paper, we give necessary and sufficient conditions for the space B_1(X) of first Baire class functions on a Tychonoff space X, with pointwise topology, to be (strongly) seq…