On the submetrizability number and -weight of quasi-uniform spaces and paratopological groups
arXiv:1503.04278
Abstract
We derive many upper bounds on the submetrizability number and -weight of paratopological groups and topological monoids with open shifts. In particular, we prove that each first countable Hausdorff paratopological group is submetrizable thus answering a problem of Arhangelskii posed in 2002. Also we construct an example of a zero-dimensional (and hence regular) Hausdorff paratopological abelian group with countable pseudocharacter which is not submetrizable. In fact, all results on the -weight and submetrizability are derived from more general results concerning normally quasi-uniformizable and bi-quasi-uniformizable spaces.
22 pages, many diagrams