# \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

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.