English

Linear homeomorphisms of function spaces and the position of a space in its compactification

General Topology 2023-11-27 v2

Abstract

An old question of A.V. Arhangel'skii asks if the Menger property of a Tychonoff space XX is preserved by homeomorphisms of its function space Cp(X)C_p(X). We provide affirmative answer in the case of linear homeomorphisms. To this end, we develop a method of studying invariants of linear homeomorphisms of fuction spaces Cp(X)C_p(X) by looking at the way XX is positioned in its (\v{C}ech-Stone) compactification.

Keywords

Cite

@article{arxiv.2208.05547,
  title  = {Linear homeomorphisms of function spaces and the position of a space in its compactification},
  author = {Mikołaj Krupski},
  journal= {arXiv preprint arXiv:2208.05547},
  year   = {2023}
}