CLOSED SUBSPACES OF STAR-LINDEL¨OF AND RELATED SPACES

Abstract

We consider star-Lindel¨ofness, a common generalization of Lindel¨ofness, countable compactness and separability; also we consider some weaker properties, such as centered-Lindel¨ofness and linked-Lindel¨ofness. We show that every Tychonoff linked-Lindel¨of space is representable as a closed subspace of a Tychonoff star-Lindel¨of space and discuss the general problem which spaces are representable as (some type of) closed subspaces of star-Lindel¨of (or, equivalently, of linked-Lindel¨of) spaces.