Raushan Z. Buzyakova
On absolutely submetrizable spaces

Comment.Math.Univ.Carolin. 47,3 (2006) 483-490.

Abstract: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 Lindel\"of). This example is used to show that absolute submetrizability is not preserved by some topological operations, in particular, by free sums.

Keywords: submetrizable, absolutely submetrizable
AMS Subject Classification: 54E99, 54F99