Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4658326 | Topology and its Applications | 2015 | 15 Pages |
Abstract
For a Tychonoff space X , let ↓CF(X)↓CF(X) denote the collection of the hypographs of all continuous maps from X to [0,1][0,1] with the Fell topology. We show that for a Tychonoff k-space X , ↓CF(X)↓CF(X) is homeomorphic to c0c0 if and only if ↓CF(X)↓CF(X) is metrizable and not Baire if and only if X is a weakly locally compact and hemicompact ℵ0ℵ0-space without dense set of isolated points, where Q=[−1,1]ωQ=[−1,1]ω is the Hilbert cube, Σ={(xn)∈Q:sup|xn|<1}Σ={(xn)∈Q:sup|xn|<1} and c0={(xn)∈Σ:limxn=0}c0={(xn)∈Σ:limxn=0} are the subspaces of it.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Zhongqiang Yang, Yanmei Zheng, Jiyang Chen,