Giuseppe Di Maio, Enrico Meccariello, Somashekhar Naimpally
Symmetric Proximal Hypertopology
The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. [58], [3]-[25]([2004])
54B20 Hyperspaces
54E05 Proximity structures and generalizations
Abstract: In 1988 a new hypertopology, called \textbf{proximal

(finite) hypertopology} was discovered. It involves the use of a proximity

in the upper part but leaves the lower part the same as the lower Vietoris

topology. In 1966, the lower Vietoris topology, which involves finitely many

open sets, led to another lower topology involving locally finite families

of open sets. In this paper, we change the lower hypertopology using a

proximity and thus get a ``symmetric`` proximal hypertopology, which

includes the earlier `finite' topologies.

Keywords: Proximities, hyperspace, lower proximal hypertopology, upper proximal hypertopology, symmetric proximal hypertopology, Bombay hypertopology