Geodesic
The Metrizability of Spaces whose Diagonals have a Countable Base
Canadian mathematical bulletin, Tome 20 (1977) no. 4, pp. 513-514

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DOI

It is shown that the diagonal of X has a countable neighborhood base in X × X if and only if X is a metrizable space whose set of non-isolated points is compact.
DOI : 10.4153/CMB-1977-078-2
Mots-clés : 54E35, diagonal, neighborhood base, metrizability, compact 
Ginsburg, John. The Metrizability of Spaces whose Diagonals have a Countable Base. Canadian mathematical bulletin, Tome 20 (1977) no. 4, pp. 513-514. doi: 10.4153/CMB-1977-078-2
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     title = {The {Metrizability} of {Spaces} whose {Diagonals} have a {Countable} {Base}},
     journal = {Canadian mathematical bulletin},
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-078-2/}
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