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 ${\Cal E}$.

Keywords: $\pi$-network; ideal; $\star$-topology; semiregularization; submaximal and Volterra spaces.

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

Pages:  174$-$184     

Volume  67 ,  Issue  3 ,  2015