Mikołaj Krupski
Mikołaj Krupski: \(\kappa\)-pseudocompactness and uniform homeomorphisms of function spaces
06/12/22 08:10
Tuesday, December 6, 2022 17:00
Location: room C11-3.11
Speaker: Mikołaj Krupski (University of Warsaw)
Title: \(\kappa\)-pseudocompactness and uniform homeomorphisms of function spaces
Abstract: A Tychonoff space \(X\) is called \(\kappa\)-pseudocompact if for every continuous mapping \(f\) of \(X\) into \( {\mathbb{R}}^\kappa\) the image \(f(X)\) is compact. This notion generalizes pseudocompactness and gives a stratification of spaces lying between pseudocompact and compact spaces. It is well known that pseudocompactness of \(X\) is determined by the uniform structure of the function space \(C_p(X)\) of continuous real-valued functions on \(X\) endowed with the pointwise topology. In respect of that A.V. Arhangel'skii asked in [Topology Appl., 89 (1998)] if analogous assertion is true for \(\kappa\)-pseudocompactness. We provide an affirmative answer to this question.
Location: room C11-3.11
Speaker: Mikołaj Krupski (University of Warsaw)
Title: \(\kappa\)-pseudocompactness and uniform homeomorphisms of function spaces
Abstract: A Tychonoff space \(X\) is called \(\kappa\)-pseudocompact if for every continuous mapping \(f\) of \(X\) into \( {\mathbb{R}}^\kappa\) the image \(f(X)\) is compact. This notion generalizes pseudocompactness and gives a stratification of spaces lying between pseudocompact and compact spaces. It is well known that pseudocompactness of \(X\) is determined by the uniform structure of the function space \(C_p(X)\) of continuous real-valued functions on \(X\) endowed with the pointwise topology. In respect of that A.V. Arhangel'skii asked in [Topology Appl., 89 (1998)] if analogous assertion is true for \(\kappa\)-pseudocompactness. We provide an affirmative answer to this question.