hα-Open Sets in Topological Spaces

In our work we introduced a new type of open sets is defined as follows: If for each set that is not empty M in X, MX and M ^such that A int(AM). then A in (X,) is named h-open set. We also go through the relationship between h- open sets and a variety of other open set types as h-open sets, open sets, semi-open sets and -open sets. We proved that each h-open and open set is h-open and there is no relationship between-open sets and semi-open sets with h-open sets. Furthermore, we begin by introducing the concepts of h-continuous mappings, h-open mappings, h-irresolute mappings, and h-totally continuous mappings, We proved that each h-continuous mapping in any topological space is h-continuous mapping, each continuous mapping in any topological space is h-continuous mapping and there is no relationship between-continuous mappings and semi-continuous mappings with h-continuous mappings as well as some of its features. Finally, we look at some of the new class's separation axioms.