A NOTE ON GENERALIZED METRIZABLEPROPERTIES IN TOPOLOGICAL GROUPS

摘要

This paper is concerned with some generalized metrizable properties in topological groups.It is proved that for a topological group G and a locally compact metrizable subgroup Нof G, if the quotient space G/Н is stratifiable (resp. semi-stratiflable, k-semi-stratiflable,a a-space) then the space G is stratiflable (resp. semi-stratiflable, k-senii-stratiflable, a σ-space), which gives an affirmative answer to a question raised by A. V. Arhangel'skii and V.V. Uspenskij. Also the authors discuss the No-weakly first-countable paratopological groupswhich contain no closed copies of S_w.