Geodesic
Selections, Paracompactness and Compactness
Serdica Mathematical Journal, Tome 35 (2010) no. 4, pp. 299-328.

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In the present paper the Lindelöf number and the degree of compactness of spaces and of the cozero-dimensional kernel of paracompact spaces are characterized in terms of selections of lower semi-continuous closed-valued mappings into complete metrizable (or discrete) spaces.
Keywords: Set-Valued Mapping, Selection, Cozero-Dimensional Kernel, Compactness Degree, Lindelöf Number, Paracompact Space, Shrinking 
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     title = {Selections, {Paracompactness} and {Compactness}},
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Choban, Mitrofan M.; Mihaylova, Ekaterina P.; Nedev, Stoyan I. Selections, Paracompactness and Compactness. Serdica Mathematical Journal, Tome 35 (2010) no. 4, pp. 299-328. http://geodesic.mathdoc.fr/item/SMJ2_2010_35_4_a0/