IJPAM: Volume 112, No. 1 (2017)

Title

REMARKS ON $\delta$-OPEN SETS INDUCED BY
ENLARGEMENTS OF GENERALIZED TOPOLOGIES

Authors

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

Abstract

The concepts of $\kappa_{\mu}$-open set and enlargement $\kappa$ of a generalized topology $\mu$ were introduced by Császár [5]. In this paper, we introduce the concept of $\delta_{\mu}$-open set induced by an enlargement $\kappa$ of a generalized topology $\mu$, and we study some basic properties for the set. Moreover, we establish the relationships among $\kappa_{\mu}$-open sets, weak $\kappa_{\mu}$-open [6] and $\delta_{\kappa}$-open.

History

Received: November 18, 2016
Revised: January 10, 2017
Published: January 26, 2017

AMS Classification, Key Words

AMS Subject Classification: 54A05, 54B10, 54C10, 54D30
Key Words and Phrases: generalized topology, enlargement, $\kappa_{\mu}$-open, $\kappa_{\mu}$-regular open, weak $\kappa_{\mu}$-open, $\delta_{\kappa}$-open

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Bibliography

1
Á. Császár, Generalized open sets, Acta Math. Hungar., 75 (1997), 65-87.

2
Á. Császár, Generalized topology, generalized continuity, Acta Math. Hungar., 96 (2002), 351-357.

3
Á. Császár, Further remarks on the formular for $\gamma$-interior, Acta Math. Hungar., 113 (2006), 325-332.

4
Á. Császár, $\delta$- and $\theta$-modificatons of generalized topologies, Acta Math. Hungar., 120, No. 3 (2008), 275-279.

5
Á. Császár, Enlargements and generalized topologies, Acta Math. Hungar., 120, No. 4 (2008), 351-354.

6
Y. K. Kim and W. K. Min, Further remarks on Enlargements of generalized topologies, Acta Math. Hungar., 135, No. 1 (2012), 184–191.

7
Y. K. Kim and W. K. Min, $\sigma$-structures and quasi-enlarging operations, International Journal of Pure and Applied Mathematics, 86, No. 5 (2013), 791-798.

How to Cite?

DOI: 10.12732/ijpam.v112i1.11 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: 112
Issue: 1
Pages: 137 - 143


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