# Article

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Keywords:
zeroset diagonal; regular $G_\delta$-diagonal; submetrizable; countable extent
Summary:
We show that if $X^2$ has countable extent and $X$ has a zeroset diagonal then $X$ is submetrizable. We also make a couple of observations regarding spaces with a regular $G_\delta$-diagonal.
References:
[ARH] Arhangelskii A.V.: On a class of spaces containing all metric spaces and all locally compact spaces. Mat. Sb 67 (1965), English Translation: Amer. Math. Soc. Transl. 92 (1970), 1-39. MR 0190889
[ENG] Engelking R.: General Topology. Sigma Series in Pure Mathematics, 6, Heldermann, Berlin, revised ed., 1989. MR 1039321 | Zbl 0684.54001
[FRW] Fleissner W.G., Reed G.M., Wage M.L.: Normality versus countable paracompactness in perfect spaces. Bull. Amer. Math. Soc. 82 4 (1976), 635-639. MR 0410665 | Zbl 0332.54018
[KAR] Karpov A.N.: Countable products of Čech-complete linearly Lindelöf and initially-compact spaces. Vestnik Moskov. Univ. Ser. I Mat. Mekh. (2000), 5 7-9, 67. MR 1799346 | Zbl 0984.54006
[MAR] Martin H.W.: Contractibility of topological spaces onto metric spaces. Pacific J. Math. 61 (1975), 1 209-217. MR 0410685 | Zbl 0304.54026

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