MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
Topology generated by cluster systems
R. Thangamariappan and V. Renukadevi

Abstract

In this paper, we prove that $(X,\tau)$ and the new topology $(X,\tau_{\Cal E})$ have the same semiregularization if ${\Cal E}$ is a $\pi$-network in $X$ with the property ${\Cal H}$. Also, we discuss the properties of ${\Cal E},\tau_{\Cal E}$ and study generalized Volterra 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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Keywords: $\pi$-network; ideal; $\star$-topology; semiregularization; submaximal and Volterra spaces.

MSC: 54A05, 54A10, 54F65, 54E99

Pages:  174--184     

Volume  67 ,  Issue  3 ,  2015