Some Characterizations of Open, Closed, and Continuous Mappings

Abstract

We obtain new characterizations of open maps in terms of closures, of closed maps in terms of interiors, and of continuous maps in terms of interiors. Further open (closed) onto maps 𝑓∶𝑋→𝑌 are described in terms of images under 𝑓 of certain closed (open) sets in 𝑋. Continuity of (onto) maps is also characterized in terms of saturated sets.