Fell topology on the hyperspace of a non-Hausdorff space |
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| Authors: | Ji-Cheng Hou Paolo Vitolo |
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| Institution: | (1) Department of Mathematics, Dalian Nationalities University, No. 18 Liao He Western Road, Dalian Economic and Development Zone, 116600 Liaoning, People’s Republic of China;(2) Dipartimento di Matematica e Informatica, Università della Basilicata, viale dell’Ateneo Lucano 10, Contrada Macchia Romana, 85100 Potenza, Italy |
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| Abstract: | 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 and of G. Beer
to the general case.
Project 10251002 supported by National Natural Science Foundation of China. |
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| Keywords: | Hyperspace Fell topology Non-Hausdorffness Saturation Countability axioms Topological convergence |
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