Geodesic
On absolutely submetrizable spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 3, pp. 483-490.

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We introduce a notion of absolute submetrizability (= ``every Tychonoff subtopology is submetrizable'') and investigate its behavior under basic topological operations. The main result is an example of an absolutely submetrizable space that contains an uncountable set of isolated points (hence the space is neither separable nor hereditarily Lindelöf). This example is used to show that absolute submetrizability is not preserved by some topological operations, in particular, by free sums.
Classification : 54E35, 54E99, 54F99
Keywords: submetrizable; absolutely submetrizable 
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Buzyakova, Raushan Z. On absolutely submetrizable spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 3, pp. 483-490. http://geodesic.mathdoc.fr/item/CMUC_2006__47_3_a10/