\kappa-pseudocompactness and uniform homeomorphisms of function spaces

Speaker(s)

Mikołaj Krupski

Affiliation

University of Warsaw

Date

Nov. 9, 2022, 4:15 p.m.

Room

room 5050

Seminar

Topology and Set Theory Seminar

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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.

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