A Novel Class of Separation Axioms, Compactness, and Continuity via <i>C</i>-Open Sets

Abstract

In this paper, we originate a new class of open sets, namely C-open sets, and we review its important properties. Then, some separation axioms of C-open sets are introduced and investigated. In addition, we define the so-called C-compact and C′-compact spaces via C-open sets, and the theorems based on them are discussed with counterexamples. Moreover, we entitle the C-continuous and C′-continuous functions by applying C-open sets. In particular, several inferred properties of them and their connection with the other topological spaces are studied theoretically. Many examples are given to explain the concepts lucidly. The results established in this research paper are new in the field of topology.

Keywords

• <tt>C</tt>-open set
• <tt>C</tt>-regular space
• <tt>C</tt>-normal space
• <tt>C</tt>-compact space
• <tt>C</tt>′-compact space
• <tt>C</tt>-continuous function