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May 2017 Strongly Generalized Neighborhood Systems
Murad Arar
Missouri J. Math. Sci. 29(1): 43-49 (May 2017). DOI: 10.35834/mjms/1488423701

Abstract

In this paper we define strongly generalized neighborhood systems (in brief strongly $GNS$) and study their properties. It's proved that every generalized topology $\mu$ on $X$ gives a unique strongly $GNS$ $\psi_{\mu}:X\rightarrow \exp{(\exp{X})}$. We prove that if a generalized topology $\mu$ is given, then $\mu_{\psi_{\mu}}=\mu$; and if a strongly $GNS $ $\psi$ is given, then $\psi_{\mu_{\psi}}=\psi$. Strongly $(\psi_{1},\psi_{2})$-continuity is defined. We prove that $f:X\rightarrow Y$ is strongly $(\psi_{1},\psi_{2})$-continuous if and only if it is $(\mu_{\psi_{1}},\mu_{\psi_{2}})$-continuous.

Citation

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Murad Arar. "Strongly Generalized Neighborhood Systems." Missouri J. Math. Sci. 29 (1) 43 - 49, May 2017. https://doi.org/10.35834/mjms/1488423701

Information

Published: May 2017
First available in Project Euclid: 2 March 2017

zbMATH: 1370.54002
MathSciNet: MR3619775
Digital Object Identifier: 10.35834/mjms/1488423701

Subjects:
Primary: 54A05

Rights: Copyright © 2017 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.29 • No. 1 • May 2017
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