On remainders of locally s-spaces

Abstract

We study the remainders of locally s-spaces and locally Lindelöf Σ-spaces. It is proved that a space X is a locally s-space if and only if every (some) remainder Y of X is a Lindelöf Σ-space outside of some compact subspace F of Y. Some corollaries about this statement are presented. It is showed that if a locally s-space X has a remainder Y with a Gδ⁎-diagonal, then X is an s-space and Y has a countable network. It is also proved that every remainder Y of a locally Lindelöf Σ-space X is an s-space outside of some compact subspace F of Y. In addition, some properties about locally s-spaces are investigated.