Geodesic
Generalized tri-quotient maps and Čech-completeness
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 1, pp. 187-194.

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For a topological space $X$ let $\Cal K (X)$ be the set of all compact subsets of $X$. The purpose of this paper is to characterize Lindelöf Čech-complete spaces $X$ by means of the sets $\Cal K (X)$. Similar characterizations also hold for Lindelöf locally compact $X$, as well as for countably $K$-determined spaces $X$. Our results extend a classical result of J. Christensen.
Classification : 54C10, 54C60
Keywords: Čech-complete spaces; Lindelöf spaces; tri-quotient maps 
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Dube, Themba; Valov, Vesko. Generalized tri-quotient maps and Čech-completeness. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 1, pp. 187-194. http://geodesic.mathdoc.fr/item/CMUC_2001__42_1_a13/