Abstract

For the hyperspace of non-empty closed sets of a quantale-valued metric space, we define a quantale-valued convergence tower which generalizes the classical Wijsman convergence. We characterize this quantale-valued convergence tower by a quantale-valued neighbourhood tower and show that it is uniformizable. Finally we study compactness and completeness of the quantale-valued Wijsman convergence tower.

Keywords: Quantale-valued metric; probabilistic metric; quantale-valued convergence; hyperspace; Wijsman convergence; Wijsman topology.

MSC: 54A20, 54A40, 54B20, 54E35, 54E70

Pages:  191$-$208     

Volume  73 ,  Issue  3 ,  2021