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
${\Cal E}$. ![Creative Commons License](https://i.creativecommons.org/l/by/4.0/80x15.png)
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