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

2022/08/10 by Krupski, Mikołaj
#54B20 #54D20 #54D40 #91A44 #FOS: Mathematics #General Topology (math.GN) #Primary: 54C35 #Secondary:54C60

paper · doi:10.48550/arxiv.2208.05547

Abstract

An old question of A.V. Arhangel'skii asks if the Menger property of a Tychonoff space X is preserved by homeomorphisms of its function space 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 C_p(X) by looking at the way X is positioned in its (Čech-Stone) compactification.

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