Abstract
The purpose of this work is to introduce and study a new topological property called epi-complete-regularity. A space (X, T) is called an epi-completely-regular space if there exists a topology T ' on X which is coarser than T such that (X, T ') is Tychonoff. This new property is investigated and some examples are presented in this work to illustrate its relationships with other kinds of normality and complete-regularity. 2020 Mathematics Subject Classifications: 54A10, 54B10, 54C10, 54D10, 54D20, 54D15, 54D70