Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4658439 | Topology and its Applications | 2014 | 14 Pages |
Abstract
For an infinite 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 shall prove that, if âCF(X) is metrizable, then there exists a copy MQ of the Hilbert cube Q=[â1,1]Ï such that âCF(X) is homotopy dense in MQ, that is, there exists a homotopy H:MQÃ[0,1]âMQ such that H(y,0)=y and H(y,t)ââCF(X) for every yâMQ and tâ(0,1]. We also give methods to construct non-metrizable spaces X such that âCF(X) are metrizable.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Zhongqiang Yang, Pengfei Yan,