• Journal of the Chungcheong Mathematical Society
• /
• v.29 no.3
• /
• pp.397-416
• /
• 2016

This paper is devoted to the study of various notions of almost openness and almost homeomorphisms and the characterization of some of them in terms of the relative interior operator. Generally, openness (or quasi-openness) for a continuous map f is well known. We define openness (or quasi-openness) at a point x using the relative interior operator and characterize that a continuous map f is almost open, almost quasi-open, almost embedding and almost homeomorphsims.