Normality and paracompactness in subsets of product spaces
We provide a necessary and sufficient condition under which a generalized ordered topological product (GOTP) of two GO-spaces is monotonically Lindelöf.
We give a characterization of normal and countably paracompact spaces via continuous set-avoiding selections.
Blum and Swaminathan [Pacific J. Math. 93 (1981), 251–260] introduced the notion of -fixedness for set-valued mappings, and characterized realcompactness by means of continuous selections for Tychonoff spaces of non-measurable cardinal. Using their method, we obtain another characterization of realcompactness, but without any cardinal assumption. We also characterize Dieudonné completeness and Lindelöf property in similar formulations.