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1976•Canadian Journal of MathematicsOpen access

A Collectionwise Hausdorff, Non-Normal Moore Space

Michael L. Wage

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Abstract

A topological space X is said to be collectionwise Hausdorff if every discrete collection of points of X can be simultaneously separated by a collection of pairwise disjoint open sets. The question of whether there exists a collectionwise Hausdorff, non-normal Moore space was first asked by R. L. Moore. In 1964, J. M. Worrell announced that such a space did indeed exist (see [7]), but his proof has never appeared in print.

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A topological space X is said to be collectionwise Hausdorff if every discrete collection of points of X can be simultaneously separated by a collection of pairwise disjoint open sets. The question of whether there exists a collectionwise Hausdorff, non-normal Moore space was first asked by R. L. Moore. In 1964, J. M. Worrell announced that such a space did indeed exist (see [7]), but his proof has never appeared in print.

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Available abstract

A topological space X is said to be collectionwise Hausdorff if every discrete collection of points of X can be simultaneously separated by a collection of pairwise disjoint open sets. The question of whether there exists a collectionwise Hausdorff, non-normal Moore space was first asked by R. L. Moore. In 1964, J. M. Worrell announced that such a space did indeed exist (see [7]), but his proof has never appeared in print.

Key concepts: Normal space, Mathematics, Hausdorff space, Disjoint sets, Paracompact space, Pairwise comparison, Space (punctuation), Urysohn and completely Hausdorff spaces

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