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Open AccessArticle

On Generalized Closed Sets and Generalized Pre-Closed Sets in Neutrosophic Topological Spaces

by Wadei Al-Omeri 1,*,†,‡ and Saeid Jafari 2,‡
1
Department of Mathematics, Al-Balqa Applied University, Salt 19117, Jordan
2
Department of Mathematics, College of Vestsjaelland South, Herrestraede 11, 4200 Slagelse, Denmark
*
Author to whom correspondence should be addressed.
Current address: Department of Mathematics, Al-Balqa Applied University, Salt 19117, Jordan.
These authors contributed equally to this work.
Mathematics 2019, 7(1), 1; https://doi.org/10.3390/math7010001
Received: 17 November 2018 / Revised: 11 December 2018 / Accepted: 13 December 2018 / Published: 20 December 2018
(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)
In this paper, the concept of generalized neutrosophic pre-closed sets and generalized neutrosophic pre-open sets are introduced. We also study relations and various properties between the other existing neutrosophic open and closed sets. In addition, we discuss some applications of generalized neutrosophic pre-closed sets, namely neutrosophic p T 1 2 space and neutrosophic g p T 1 2 space. The concepts of generalized neutrosophic connected spaces, generalized neutrosophic compact spaces and generalized neutrosophic extremally disconnected spaces are established. Some interesting properties are investigated in addition to giving some examples. View Full-Text
Keywords: neutrosophic topology; neutrosophic generalized topology; neutrosophic generalized pre-closed sets; neutrosophic generalized pre-open sets; neutrosophic p T 1 2 space; neutrosophic g p T 1 2 space; generalized neutrosophic compact and generalized neutrosophic compact neutrosophic topology; neutrosophic generalized topology; neutrosophic generalized pre-closed sets; neutrosophic generalized pre-open sets; neutrosophic p T 1 2 space; neutrosophic g p T 1 2 space; generalized neutrosophic compact and generalized neutrosophic compact
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Al-Omeri, W.; Jafari, S. On Generalized Closed Sets and Generalized Pre-Closed Sets in Neutrosophic Topological Spaces. Mathematics 2019, 7, 1.

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