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.

中文翻译：

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无处不变的映射族和可解析性

如果X是拓扑空间并且Y是任意集合，那么我们称从X到Y 的映射族$\mathcal {F}$没有常数，如果对于X中的每个非空开集U都有$f \in \ mathcal {F}$与$|f[U]|> 1$，即f在U上不是常数。我们证明了以下结果，该结果改进了文献中的几个早期结果。

如果X是一个拓扑空间，其中$C(X)$ （ X到$\mathbb {R}$的所有连续映射族）在任何地方都不是常数，并且X具有由连通集组成的$\pi $基，则X是$\mathfrak {c}$可解析的。