DOI: 10.14704/nq.2022.20.8.NQ44794

On 𝑻𝐠𝐩Topological Space and Some Generalized Closed Sets

MarwahMunther Hassan, Ali Khalaf Hussain

Abstract

The investigation continues the study of pre-closed sets and of generalized pre-closed sets in a topological space. Our main goal of this paper is to determine the results of links between different generalized types of closed sets. Through this we use pre-closed sets and their generalizations, therefore we are able to produce profiles for specific known classes of topological spaces, by establishing relationships between various generalized-closed sets will lead us to define new class of topological called 𝑇𝑔𝑝 − space. Moreover, we study this type of topological space and discussed the relationship with other spaces. Some of their properties have also been invested. As well as shows the relationships between 𝑇1/2 − space with this space, and also introduced an extremely disconnected space, add to the above we discussed some properties, theory, corollary, and examples

Keywords

pg-closed set, pg-open set,𝑇𝑔𝑝 − space, 𝑇1/2 -space, extremely disconnected space, gsp-closed set

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