INJECTIVITY VERSUS DENSE INJECTIVITY IN TOPOLOGICAL SPACES

INJECTIVITY VERSUS DENSE INJECTIVITY IN TOPOLOGICAL SPACES

An injective space is a topological space with a strong extension property for continuous maps with values on it. The topological characterizations by injectivity turns out to follow from the algebraic characterizations and general category theory (Es- cardo 1998). In this paper we study injectivity in the context of topologicalg spaces. We show that dense injective spaces are precisely the injective spaces and every injective space is compact space. This way we obtain enriched versions of known results about injective topological spaces and obtain new proofs and new char- acterizations of topological spaces by injectivity.