Type: Article

Baire property and web-adjacent spaces

Salvador García-Ferreira; Valentin Gutev;

Abstract:

We introduce the concept of web-adjacent spaces X and Y, which is motivated by a construction of Krom [7]. The purpose of the paper is to generalize the Krom's result [7] by showing that if X and Y are web-adjacent spaces, then X is a Baire space if and only if Y is a Baire space. Further, we demonstrate that, for web-adjacent spaces X and Y, the corresponding Vietoris hyperspaces F(X) and F(Y) are also web-adjacent, consequently F(X) is Baire if and only if F(Y) is Baire. This refines the answer to a question of McCoy [8].