This article is cited in 1 paper

MATHEMATICS

On a class of homeomorphisms of function spaces preserving the Lindelöf number of domains

V. R. Lazarev

Tomsk State University, Tomsk, Russian Federation

Abstract: We consider the class of all homeomorphisms between the function spaces of the form $C_p(X)$, $C_p(Y)$ such that the images of $Y$ and $X$ under their dual and, respectively, inverse dual mappings consist of finitely supported functionals. We prove that if a homeomorphism belongs to this class, then Lindelöf numbers $l(X)$ and $l(Y)$ are equal. This result generalizes the known theorem of A. Bouziad for linear homeomorphisms of function spaces.

Keywords: Lindelöf number, function space, pointwise convergence topology, finite support property.

UDC: 515.12

MSC: 54C35

Received: 19.12.2022
Accepted: December 4, 2023

Language: English

DOI: 10.17223/19988621/86/12