IJPAM: Volume 100, No. 2 (2015)

$\sigma$-$\beta$-OPEN SETS ON $\sigma$-STRUCTURES

Young Key Kim$^1$, Won Keun Min$^2$
$^1$Department of Mathematics
MyongJi University
Youngin, 449-728, KOREA
$^2$Department of Mathematics
Kangwon National University
Chuncheon, 200-701, KOREA

Abstract. The purpose of this paper is to study $\sigma$-$\beta$-open sets. Firstly, we define the $\sigma$-$\beta$-open sets and some basic properties of them. Secondly, we introduce the notions of $\sigma$-$\beta$-continuous functions and $\sigma$-$\beta$-open($\sigma$-$\beta$-closed) functions, and investigate characterizations for such functions by using the $\sigma$-interior, $\sigma$-closure, $\sigma$-$\beta$-interior and $\sigma$-$\beta$-closure operators. Finally, we investigate the relationships among $\sigma$-continuity and $\sigma$-semicontinuity, $\sigma$-precontinuity and $\sigma$-$\beta$-continuity.

Received: September 13, 2014

AMS Subject Classification: 54C08

Key Words and Phrases: $\sigma$-preopen, $\sigma$-semiopen, $\sigma$-$\beta$-open, $\sigma$-continuous, $\sigma$-precontinuous, $\sigma$-semicontinuous, $\sigma$-$\beta$-continuous

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DOI: 10.12732/ijpam.v100i2.5 How to cite this paper?

International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 100
Issue: 2
Pages: 225 - 233

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