IJPAM: Volume 115, No. 2 (2017)

Title

NEW CLASSES OF MAPPINGS AND
SEPARATION AXIOMS INDUCED BY $P_S$-OPEN sets

Authors

Baravan A. Asaad
Department of Mathematics
Faculty of Science
University of Zakho
Kurdistan Region, IRAQ

Abstract

An operation $\gamma$ on $P_SO(X)$ is a mapping $\gamma \colon P_SO(X)$ $\rightarrow$ $P(X)$ such that $U \subseteq \gamma(U)$ for every $U\in P_SO(X)$. A nonempty set $A$ of $X$ is said to be $P_S^\gamma$-open if for each $x \in A$, there exists an $P_S$-open set $U$ such that $x \in U$ and $\gamma(U) \subseteq A$ [2]. This paper is to continue the study of an operation $\gamma$ on $P_SO(X)$ and the concept of $P_S^\gamma$-open sets of $(X,\tau)$. Using this operation and this set, we introduce the concept of $P_S^\gamma$-generalized closed sets and then investigate some of its properties. In addition, more separation axioms $P_S^\gamma$-$T'_n$ spaces ( $n \in \{0,\frac{1}{2}, 1, 2\}$) have been investigated. Finally, some main characterizations of $P_S$- $(\gamma,\beta)$-continuous mappings with $P_S^\beta$-closed graphs have been obtained.

History

Received: January 26, 2017
Revised: May 2, 2017
Published: July 14, 2017

AMS Classification, Key Words

AMS Subject Classification: 54A05, 54A10, 54C05, 54C10, 54D10
Key Words and Phrases: $P_S^\gamma$-open sets, $P_S^\gamma$-$g$.closed sets, $P_S^\gamma$-$T'_n$ spaces ( $n \in \{0,\frac{1}{2}, 1, 2\}$), $P_S$- $(\gamma,\beta)$-continuous mappings, $P_S^\beta$-closed graphs

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How to Cite?

DOI: 10.12732/ijpam.v115i2.10 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 115
Issue: 2
Pages: 327 - 344


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