Pure Mathematics for Theoretical Computer Science PMTCS 2995-3162 10.54216/PMTCS https://www.americaspg.com/journals/show/2545 2023 2023 Al-Farahidi Universiry, College of engineering, Iraq Ahmed Ahmed The main aim of this paper is to study new class of continuous function is called  – continuous function. for this aim, the nation of - open and pre – open sets and  - compact space are introduced. and we shall study the relationship between  – continuous and pc– continuous functions. 2024 2024 20 23 10.54216/PMTCS.030103 https://www.americaspg.com/articleinfo/40/show/2545