Weak separation axioms and weak covering properties (Q719728)

The following results typify the nature of the theorems established in this paper: Result 1. On weakly subparacompact Hausdorff spaces with rudimentary normality, regularity = normality = countable paracompactness. Result 2. Weakly subparacompact, collectionwise \(\sigma\)-normal spaces are screenable. Also, weakly subparacompact, strongly collectionwise \(\sigma\)-normal spaces are semiparacompact. Result 3. On locally connected, locally compact Hausdorff spaces, weak\(^*\) subparacompactness + \(c\)-collectionwise \(\varepsilon\)-normality + rudimentary normality \(\Rightarrow\) paracompactness. Result 4. Weakly subparacompact, countably compact spaces are compact. Also, weakly subparacompact, \(\omega_1\)-compact spaces are Lindelöf.