On θ -Hurewicz and α -Hurewicz Topological Spaces

In this paper, we introduced α -Hurewicz and θ -Hurewicz properties in a topological space X and investigated their relationship with other selective covering properties. We have shown that for any extremally disconnected semi-regular spaces, the properties: Hurewicz, semi-Hurewicz, α -Hurewicz, θ -Hurewicz, almost-Hurewicz, nearly Hurewicz and mildly Hurewicz are equivalent. We have also proved that for an extremally disconnected space X, every finite power of X has the 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 have shown that if X is a mildly Hurewicz subspace of ω ω , than X is bounded.