Geodesic
Some results on spaces with $\aleph_1$-calibre
Commentationes Mathematicae Universitatis Carolinae, Tome 57 (2016) no. 1, pp. 131-134.

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We prove that, assuming \emph{CH}, if $X$ is a space with $\aleph_1$-calibre and a zeroset diagonal, then $X$ is submetrizable. This gives a consistent positive answer to the question of Buzyakova in Observations on spaces with zeroset or regular $G_\delta$-diagonals, Comment. Math. Univ. Carolin. 46 (2005), no. 3, 469--473. We also make some observations on spaces with $\aleph_1$-calibre.
DOI : 10.14712/1213-7243.2015.154
Classification : 54D20, 54E35
Keywords: $\aleph_1$-calibre; star countable; zeroset diagonal 
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Xuan, Wei-Feng; Shi, Wei-Xue. Some results on spaces with $\aleph_1$-calibre. Commentationes Mathematicae Universitatis Carolinae, Tome 57 (2016) no. 1, pp. 131-134. doi : 10.14712/1213-7243.2015.154. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.154/

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