Geodesic
On Metrizability of Topological Spaces
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 795-804

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

Our present work is divided into three sections. In §2 we study the metrizability of spaces with a G δ-diagonal (see Definition 2.1). In §3 we study the metrization of topological spaces by means of collections of (not necessarily continuous) real-valued functions on a topological space. Our efforts, in §§2 and 3, are directed toward answering the following question: “Is every normal, metacompact (see Definition 2.4) Moore space a metrizable space?” which still remains unsolved. (However, Theorems 2.12 through 2.15 and Theorem 3.1 may be helpful in answering the preceding question.) In §4 we prove an apparently new necessary and sufficient condition for the metrizability of the Stone-Čech compactification of a metrizable space and hence for the compactness of a metric space. 
Borges, Carlos J. R. On Metrizability of Topological Spaces. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 795-804. doi: 10.4153/CJM-1968-078-1
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