G-Uniformities,LR-Proximities and Hypertopologies |
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Authors: | D Di Caprio E Meccariello |
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Institution: | (1) Facoltà di Scienze Dipartimento di Matematica Complesso Universitario di Via Vivaldi, Seconda Università Degli Studi di Napoli, 81100 Caserta, Italia;(2) Facoltà di Ingegneria, Università Degli Studi del Sannio, Piazza Roma, Palazzo Bosco Lucarelli, 82100 Benevento, Italia |
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Abstract: | We look closely at the relationships between hit-and-miss and proximal hit-and-miss -topologies, in the setting of proximity spaces. We provide equivalent conditions that force comparisons among proximal hit-and-miss -topologies determined by different proximities. We pay attention to these topologies when consists of the family of all closed balls of a proximity space, and we study their interplay with the Wijsman convergence expressed in proximity spaces. Finally we study the supremum of all Wijsman convergences and of all proximal ball topologies when X is at most regular, and the infimum of all Wijsman convergences when X is at least Tychonoff. |
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