Resumen de The regions below compact-supported upper semicontinuous maps

Lili Zhang, Zhongqiang Yang

• Let X be a non-compact locally compact separable metric space. We use USCC(X) to denote the family of the regions below of all compact-supported upper semi-continuous maps from X to I=[0,1]. We may topologize USCC(X) by the Hausdorff metric. It is proved in this paper that USCC(X) is homemorphic to S if X is non-discrete, and USCC(X) is homemorphic to Qf if X is discrete, where S={(xn) in Q: sup|xn|<1} is the radial interior of the Hilbert cube Q=[-1,1]? and Qf ={(xn) in Q : xn=0 except for finitely many n}