Collectionwise normal space

In mathematics, a topological space $X$ is called collectionwise normal if for every discrete family F_i (i ∈ I) of closed subsets of $X$ there exists a pairwise disjoint family of open sets U_i (i ∈ I), such that F_i ⊂ U_i. A family $\mathcal{F}$ of subsets of $X$ is called discrete when every point of $X$ has a neighbourhood that intersects at most one of the sets from $\mathcal{F}$ . An equivalent definition demands that the above U_i (i ∈ I) are themselves a discrete family, which is stronger than pairwise disjoint.

单词	Collectionwise normal space
释义	Collectionwise normal space 英语百科 Collectionwise normal space In mathematics, a topological space $X$ is called collectionwise normal if for every discrete family F_i (i ∈ I) of closed subsets of $X$ there exists a pairwise disjoint family of open sets U_i (i ∈ I), such that F_i ⊂ U_i. A family $\mathcal{F}$ of subsets of $X$ is called discrete when every point of $X$ has a neighbourhood that intersects at most one of the sets from $\mathcal{F}$ . An equivalent definition demands that the above U_i (i ∈ I) are themselves a discrete family, which is stronger than pairwise disjoint.
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