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.