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Sem. Topologia i T. Mnogości

 

\kappa-pseudocompactness and uniform homeomorphisms of function spaces


Prelegent: Mikołaj Krupski

2022-11-09 16:15

A Tychonoff space X is called \kappa-pseudocompact if for every continuous mapping f of X into 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.