Exponential topology
type: Item
instance of: scholarly article
title: Exponential topology
zbMATH Open document ID: 0544.54006
DOI: 10.1007/BF01088924
author: R. S. Linichuk
author: V. M. Safonov
published in: Ukrainian Mathematical Journal
publication date: 1983-01-01T00:00:00Z
review text: There are examinated some properties of the hyperspace \(\psi\) X of all nonempty subsets of a topological space X with the exponential topology. For example, the authors describe a closure of a singleton of \(\psi\) X for a \(T_ 1\)-space X, prove that a singleton A of \(\psi\) X formed by closed points of X is \(\psi\) X-closed iff A is X-closed (without any assumption concerning X), show that X is \(T_ 0\) iff X is \(T_{1/2}\) (any singleton is either open or closed) and describe some other basic properties of \(\psi\) X with respect to corresponding properties of X.
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 54D10
zbMATH DE Number: 3866152
zbMATH Keywords: T-1/2-space
zbMATH Keywords: exponential topology
reviewed by: J. Chvalina
MaRDI profile type: Publication
cites work: Hyperextensions of multivalued mappings and spectral representation of certain hyperspaces
cites work: Topologies on Spaces of Subsets
full work available at URL: https://doi.org/10.1007/bf01088924
OpenAlex ID: W4244406127
description: scientific article; zbMATH DE number 3866152