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Fell topology on the hyperspace of a non-Hausdorff space. (English) Zbl 1232.54016

Summary: Fell topology is very widely used today, even in metric spaces; but J. Fell introduced it in a non-Hausdorff context in the connection with the theory of \(C ^{*}\)-algebras. In spite of this, it has been studied only on the hyperspace of a Hausdorff space, except for the first results due to Fell himself. The present paper aims to fill this gap, in particular extending some results of H. Poppe [Fundam. Math. 59, 159–169 (1966; Zbl 0139.40404)] and of G. Beer [Set-Valued Anal. 1, No. 1, 69-80 (1993; Zbl 0810.54010)] to the general case.

MSC:

54B20 Hyperspaces in general topology
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