Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5777855 | Topology and its Applications | 2017 | 14 Pages |
Abstract
For a Tychonoff space X, let âCF(X) denote the collection of the hypographs of all continuous maps from X to [0,1] with the Fell topology. We show that, for a Tychonoff non-discrete k-space X, the function space âCF(X) is homeomorphic to c0âª(QâΣ) if âCF(X) is metrizable and the set of isolated points of X is dense in X, where Q=[â1,1]N is the Hilbert cube, Σ={(xn)âQ:supâ¡|xn|<1} and c0={(xn)âΣ:limâ¡xn=0} are its subspaces. Combining results in the previous papers of the series, we give the topological classification for all metrizable function spaces âCF(X) of k-spaces X.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Hanbiao Yang, Zhongqiang Yang, Yanmei Zheng,