On $θ$-Hurewicz and $α$-Hurewicz Topological spaces
In this paper, we introduced $α$-Hurewicz $\&$ $θ$-Hurewicz properties in a topological space $X$ and investigated their relationship with other selective covering properties. We have shown that for an extremally disconnected semi-regular spaces, the properties: Hurewicz, semi-Hurewicz, $α$-Hurewicz, $θ$-Hurewicz, almost-Hurewicz, nearly Hurewicz and midly Hurewicz are equivalent. We have also proved that for an extremally disconnected space X, every finite power of X has $θ$-Hurewicz property if and only if X has the selection principle $U_{fin}(θ$-$Ω, θ$-$Ω)$. The preservation under several types of mappings of $α$-Hurewicz and $θ$-Hurewicz properties are also discussed. Also, we showed that, if $X$ is a mildly Hurewicz subspace of $ ω^ω$, than $X$ is bounded.