DUALITIES FOR LOWER SEMICONTINUOUS MAPS IN THE FRAMEWORK OF INTERIOR SPACES

摘要

The aim of this paper is to study dualities for lower semicontinuous maps in the framework of interior spaces. For an interior space (X, O(X)) and a complete lattice L, let [X -> L] be the set of all lower semicontinuous maps of (X, O(X)), that is, the set of all continuous maps from (X, O(X)) to (L, p nu(L)), where p nu(L) = {Ldown arrow broken vertical bar r is an element of L}. We get three dualities for [X -> L]: