Topological structure of the space of lower semi-continuous functions
Katsuro Sakai, Shigenori Uehara (2006)
Commentationes Mathematicae Universitatis Carolinae
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Let be the space of all lower semi-continuous extended real-valued functions on a Hausdorff space , where, by identifying each with the epi-graph , is regarded the subspace of the space of all closed sets in with the Fell topology. Let We show that is homeomorphic to the Hilbert cube if and only if is second countable, locally compact and infinite. In this case, it is proved that is homeomorphic to (resp. ) if is compact (resp. is non-compact), where is...