In our work a new type of open sets is introduced and defined as follows: If for each set that is not empty M in 𝑋, 𝑀 ≠ 𝑋 and 𝑀 ∈ 𝜏 ∝ such that 𝐴 ⊆ int(𝐴 ∪ 𝑀), then A in (𝑋, 𝜏) 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.