Spaces in which every dense subset is a G_δ

Abstract

A topological space X is called a DG_δ-space if every subset of X is a G_δ-set in its closure. In this paper we study DG_δ-spaces that contains subspaces in which every dense subset is open and spaces in which every subset is a G_δ . We give some new results in these classes of topological spaces.

Mathematics Subject Classification (2010):

• Primary 54C30
• 54C40;
• Secondary 54C05

Key words:

• Almost GP-spaces
• DG_δ -spaces, nodef spaces
• FI-spaces
• σ-left-separated space
• open-hereditarily irresolvable spaces
• submaximal spaces
• DG_δ right topological groups
• Q-set spaces