Topological classification of function spaces with the Fell topology. I.
type: Item
instance of: scholarly article
title: Topological classification of function spaces with the Fell topology. I.
zbMATH Open document ID: 1305.54029
published in: Topology and its Applications
publication date: 2014-11-14T00:00:00Z
review text: Let \(X\) be a Tychonoff topological space, \(L\) a subset of the real line \(\mathbb R\) with the usual order and topology, and \(USC(X, L)\) (respectively, \(C(X, L)\)) the set of all upper semi-continuous maps (respectively, continuous maps) from \(X\) to the subspace \(L\) of \(\mathbb R\). For every \(f\in USC(X, L)\), the closed set \(\downarrow f = \{(x, t) \in X\times L : t \leq f(x)\}\subseteq X\times L\) is called the hypograph of \(f\). By \(\downarrow C_F(X)\) the authors denote the collection of the hypographs of all continuous maps from \(X\to [0, 1]\) with the Fell topology. In this interesting paper they prove the following main theorem: { Main Theorem.} For every weakly locally compact and hemicomapct infinite \(\aleph_0\)-space \(X\), there exists a space \(M^Q\) such that \(M^Q\approx Q\) and \(\downarrow C_F(X)\) can be imbedded to \(M^Q\) as a homotopy dense set.
reviewed by: Dimitris Georgiou
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 54B20
zbMATH DE Number: 6369786
zbMATH Keywords: the Fell topology
zbMATH Keywords: the Hilbert cube
zbMATH Keywords: homotopy dense
zbMATH Keywords: metrizable
zbMATH Keywords: continuous map
author: Zhongqiang Yang
author: Peng-Fei Yan
MaRDI profile type: Publication
full work available at URL: j.topol.2014.09.003
OpenAlex ID: W2119167967
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DOI: 10.1016/J.TOPOL.2014.09.003
description: scientific article; zbMATH DE number 6369786