On Regular K -Bounded Spaces Admitting Only Constant Continuous Mappings into T1 Spaces of Pseudocharacter ≤ κ

Abstract

For each cardinal κ we construct an infinite κ-bounded (and hence countably compact) regular space Rκ such that for any T1 space Y of pseudocharacter ≤ κ, each continuous function f: Rκ→ Y is constant. This result resolves two problems posted by Tzannes[13] and extends results of Ciesielski and Wojciechowski [4] and Herrlich [8]. © 2020, Akadémiai Kiadó, Budapest, Hungary.