A Urysohn lemma for regular spaces

Abstract

Using the concept of m-open sets, M-regularity and M-normality are introduced and investigated. Both these notions are closed under arbitrary product. M-normal spaces are found to satisfy a result similar to Urysohn lemma. It is shown that closed sets can be separated by m-continuous functions in a regular space.

Keywords

• regularity
• normality
• m-normality
• m-regularity
• urysohn lemma