Quotients of Strongly Realcompact Groups

Abstract

A topological group is strongly realcompact if it is topologically isomorphic to a closed subgroup of a product of separable metrizable groups. We show that if H is an invariant Čech-complete subgroup of an ω-narrow topological group G, then G is strongly realcompact if and only if G/H is strongly realcompact. Our proof of this result is based on a thorough study of the interaction between the P-modification of topological groups and the operation of taking quotient groups.

Keywords

• Extension of groups
• Strongly realcompact
• Strongly Dieudonné complete
• P-modification
• Pgroup
• Quotient group