Wei-Feng Xuan, Wei-Xue Shi
Some results on spaces with $\aleph_1$-calibre

Comment.Math.Univ.Carolin. 57,1 (2016) 131-134.

Abstract: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 {\it Observations on spaces with zeroset or regular $G_\delta$-diagonals\/}, Comment. Math. Univ. Carolin. {\bf 46} (2005), no.~3, 469--473. We also make some observations on spaces with $\aleph_1$-calibre.

Keywords: $\aleph_1$-calibre; star countable; zeroset diagonal

DOI: DOI 10.14712/1213-7243.2015.154
AMS Subject Classification: 54D20 54E35