Bitopological Local Compactness and the Bitopological Fell Hyperspace
by
Bruce S. Burdick
Roger Williams University

Given a bitopological space (X, T, T*), we define two kinds of hyperspaces of (X, T, T*) - one is (2^X, L(T), U(T*)) where 2^X is the set of non-empty T-closed subsets of X, L(T) is the lower Vietoris topology for T, and U(T*) is the upper Vietoris topology for T*; the other is the Fell hyperspace (2^X, L(T), U_F(T*)), where basis elements for U_F(T*) are of the form for each O in T* for which X - O is T-compact.

Previously, we have investigated bitopological versions of compactness and sobriety which work well with the hyperspace (2^X, L(T), U(T*)). Here we look at bitopological local compactness and its consequences for the Fell hyperspace (2^X, L(T), U_F(T*)). In particular, we observe that a local compactness property of (X, T, T*) is sufficient for U_F(T*) to be the Scott topology for the order of reverse inclusion on 2^X

Date received: June 13, 1997

Copyright © 1997 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caao-19.