Topology generated by cluster systems

Authors

  • R. Thangamariappan and V. Renukadevi ANJA College (Autonomous), Sivakasi–626 124, Tamil Nadu, India Author

Keywords:

$\pi$-network, ideal, $\star$-topology, semiregularization, submaximal and Volterra spaces

Subjects:

54A05, 54A10, 54F65, 54E99

Abstract

In this paper, we prove that $(X,\tau)$ and thenew topology $(X,\tau_{\Cal E})$ have the same semiregularization if${\Cal E}$ is a $\pi$-network in $X$ with the property ${\Cal H}$. Also, wediscuss the properties of ${\Cal E},\tau_{\Cal E}$ and study generalizedVolterra spaces and discuss their properties. We show that$\tau_{\Cal E}$ coincides with the $\star$-topology for a particular${\Cal E}$.

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Published

2015-07-15

Issue

Vol. 67 No. 3 (2015): Vol. 67, Issue 3

Section

Articles

License

Copyright (c) 2015 Authors retain copyright to their work.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.