Investigation of New Notions in Topological Spaces

Abstract

In the year 1970, S. Willard introduced the General topology and in 1982, the -closed mappings. Let A be a subset of a topological space (X, and#120591; ), a pointand#61689;H. Z. Hdeib studied p in X is called a condensation point of A if for each open set B containing p, B and#8745; A is uncountable. A subset A of a topological space (X, and#964;) is called and#969;-closed if it contains all its condensation points. The complement of an and#969;-closed set is called and#969;-open. General topologists developed both the notions parallelly during the last two decades. But our interest is to investigate the results and the recent concepts that are related to and#969;-open sets and and#969;-closed sets in the sense of Hdeib. In the year 2010, E. Ekici and S. Jafari, used the interior and closure operators to define the near and closer relations in topology. Following this Chirelekha, in the year 2021, had recently investigated some new types near and closer relations in topology and bitopology. Quite recently, Samer Al-Ghour et.al.(2022) and Pmar Sasma z et.al.(2021) contributed their investigations on and#969;-open sets in the settings of theta topology and delta topology respectively. newline