Abstract: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 Lindel\"of \v Cech-complete spaces $X$ by means of the sets $\Cal K (X)$. Similar characterizations also hold for Lindel\"of locally compact $X$, as well as for countably $K$-determined spaces $X$. Our results extend a classical result of J. Christensen.
Keywords: \v Cech-complete spaces, Lindel\"of spaces, tri-quotient maps
AMS Subject Classification: 54C10, 54C60