Nowhere constant families of maps and resolvability
Canadian mathematical bulletin, Tome 67 (2024) no. 3, pp. 701-705
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If X is a topological space and Y is any set, then we call a family $\mathcal {F}$ of maps from X to Y nowhere constant if for every non-empty open set U in X there is $f \in \mathcal {F}$ 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 $\mathbb {R}$, is nowhere constant and X has a $\pi $-base consisting of connected sets then X is $\mathfrak {c}$-resolvable.
Mots-clés :
Nowhere constant family of maps, resolvable space, π-base, connected, locally connected
Juhász, István; Mill, Jan van. Nowhere constant families of maps and resolvability. Canadian mathematical bulletin, Tome 67 (2024) no. 3, pp. 701-705. doi: 10.4153/S0008439524000109
@article{10_4153_S0008439524000109,
author = {Juh\'asz, Istv\'an and Mill, Jan van},
title = {Nowhere constant families of maps and resolvability},
journal = {Canadian mathematical bulletin},
pages = {701--705},
year = {2024},
volume = {67},
number = {3},
doi = {10.4153/S0008439524000109},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439524000109/}
}
TY - JOUR AU - Juhász, István AU - Mill, Jan van TI - Nowhere constant families of maps and resolvability JO - Canadian mathematical bulletin PY - 2024 SP - 701 EP - 705 VL - 67 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4153/S0008439524000109/ DO - 10.4153/S0008439524000109 ID - 10_4153_S0008439524000109 ER -
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