Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/111395
Title: On Regular K -Bounded Spaces Admitting Only Constant Continuous Mappings into T1 Spaces of Pseudocharacter ≤ κ
Authors: Bardyla, S.
Osipov, A.
Issue Date: 2021
Publisher: Springer Science and Business Media B.V.
Springer Science and Business Media LLC
Citation: Bardyla S. On Regular K -Bounded Spaces Admitting Only Constant Continuous Mappings into T1 Spaces of Pseudocharacter ≤ κ / S. Bardyla, A. Osipov. — DOI 10.3390/plants11060741 // Acta Mathematica Hungarica. — 2021. — Vol. 163. — Iss. 1. — P. 323-333.
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.
Keywords: CONSTANT FUNCTION
COUNTABLY COMPACT SPACE
Κ-BOUNDED SPACE
URI: http://hdl.handle.net/10995/111395
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85093916840
PURE ID: 21024414
ISSN: 0236-5294
DOI: 10.3390/plants11060741
metadata.dc.description.sponsorship: The work of the first author is supported by the Austrian Science Fund FWF (Grant I 3709 N35). The work of the second author was made in the framework of research conducted at the Ural Mathematical Center.The authors acknowledge Lyubomyr Zdomskyy for his fruitful comments and suggestions. The work reported here was carried out during the visit of the second named author to the KGRC in Vienna. He wishes to thank his colleagues in Vienna.
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