Juhász, István and van Mill, Jan (2024) Nowhere constant families of maps and resolvability. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, Publis. ISSN 0008-4395
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Official URL: https://doi.org/10.4153/S0008439524000109
Abstract
If X is a topological space and Y is any set, then we call a family F of maps from X to Y nowhere constant if for every non-empty open set U in X there is f ∈ F with ∣ f [U]∣ > 1, i.e., f is not constant on U. We prove the following result that improves several earlier results in the literature. If X is a topological space for which C(X), the family of all continuous maps of X to R, is nowhere constant and X has a π-base consisting of connected sets then X is c-resolvable.
Item Type: | Article |
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Uncontrolled Keywords: | connected; resolvable space; locally connected.; nowhere constant family of maps; π- base; |
Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
SWORD Depositor: | MTMT SWORD |
Depositing User: | MTMT SWORD |
Date Deposited: | 05 Apr 2024 08:01 |
Last Modified: | 05 Apr 2024 08:01 |
URI: | https://real.mtak.hu/id/eprint/191931 |
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