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Notes on monotone Lindelöf property

Ai-Jun Xu, Wei-Xue Shi (2009)

Czechoslovak Mathematical Journal

We provide a necessary and sufficient condition under which a generalized ordered topological product (GOTP) of two GO-spaces is monotonically Lindelöf.

On a selection theorem of Blum and Swaminathan

Takamitsu Yamauchi (2004)

Commentationes Mathematicae Universitatis Carolinae

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.

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