Geodesic
Locally Compact Normal Spaces in the Constructible Universe
Canadian journal of mathematics, Tome 34 (1982) no. 5, pp. 1091-1096

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

Arhangel'skiĭ proved around 1959 [1] that, for the class of perfectly normal locally compact spaces, metacompactness and paracompactness are equivalent. It is shown to be consistent that this equivalence holds for the (larger) class of normal locally compact spaces (answering a question of Tall [8], [9]).The consistency of the existence of locally compact normal noncollectionwise Hausdorff spaces has been known since 1967. It is shown that the existence of such spaces is independent of the axioms of set theory, thus establishing that Bing's example G cannot be modified under ZFC to be locally compact.All topological spaces are assumed to be Hausdorff.First, a definition and three standard lemmata are needed. 
Watson, W. Stephen. Locally Compact Normal Spaces in the Constructible Universe. Canadian journal of mathematics, Tome 34 (1982) no. 5, pp. 1091-1096. doi: 10.4153/CJM-1982-078-8
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