Geodesic
Some Examples of Normal Moore Spaces
Canadian journal of mathematics, Tome 29 (1977) no. 1, pp. 84-92

Voir la notice de l'article provenant de la source Cambridge University Press

A normal Moore space is non-metrizable only if it fails to be ƛ-collectionwise normal for some uncountable cardinal ƛ [1].For each uncountable cardinal X we present a class of normal, locally metrizable Moore spaces and a particular space Sλ in . If there is any space of class which is not X-collectionwise normal, then Sλ is such a space. The conditions for membership in make a space in behave like a subset of a product of a Moore space with a metric space. The class is sufficiently large to allow us to prove the following. Suppose F is a locally compact, 0-dimensional Moore space (not necessarily normal) with a basis of cardinality X and M is a metric space which is O-dimensional in the covering sense. If there is a normal, not X-collectionwise normal Moore space X where X ⊂ Y × M, then Sx is a normal, not λ-collectionwise normal Moore space. 
Rudin, Mary Ellen; Starbird, Michael. Some Examples of Normal Moore Spaces. Canadian journal of mathematics, Tome 29 (1977) no. 1, pp. 84-92. doi: 10.4153/CJM-1977-008-9
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[1] 1. Bing, R. H., Metrization of topological spaces, Can. J. Math. 3 (1951), 175–186. Google Scholar

[2] 2. Fleissner, W., When normal implies collectionwise Hausdorff: consistency results, Thesis, University of California, Berkeley 1974. Google Scholar

[3] 3. Tall, F., Set-theoretic consistency results and topological theorems concerning the normal Moore space conjecture and related problems, Thesis, University of Wisconsin, Madison 1969. Google Scholar

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