Stephen Watson
Abstract
We show, for example, that normal collectionwise Hausdorff spaces which are collectionwise normal with respect to families of cardinality ${\aleph _1}$ are collectionwise normal with respect to any number of copies of $[0,1]$. We also show that normal collectionwise Hausdorff spaces are collectionwise normal with respect to scattered paracompact sets.
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We show, for example, that normal collectionwise Hausdorff spaces which are collectionwise normal with respect to families of cardinality ${\aleph _1}$ are collectionwise normal with respect to any number of copies of $[0,1]$. We also show that normal collectionwise Hausdorff spaces are collectionwise normal with respect to scattered paracompact sets.
Key concepts: Paracompact space, Hausdorff space, Cardinality (data modeling), Mathematics, Normal space, Hausdorff distance, Combinatorics, Topological space