Induced mappings on symmetric products of continua

Given a continuum X and a positive integer n, let Fn(X) be the hyperspace of all nonempty subsets of X having at most n points. Given a mapping f:X→Y between continua, we study the induced mapping fn:Fn(X)→Fn(Y) given by fn(A)=f(A) (the image of A under f). In this paper, we prove some relationships...

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Bibliographic Details
Published in:Topology and its applications 2016-12, Vol.214, p.100-108
Main Authors: Anaya, José G., Capulín, Félix, Maya, David, Orozco-Zitli, Fernando
Format: Article
Language:English
Subjects:
Continuum
Induced mapping
Symmetric product
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Summary:Given a continuum X and a positive integer n, let Fn(X) be the hyperspace of all nonempty subsets of X having at most n points. Given a mapping f:X→Y between continua, we study the induced mapping fn:Fn(X)→Fn(Y) given by fn(A)=f(A) (the image of A under f). In this paper, we prove some relationships among the mappings f and fn for the following classes of mappings: almost open, almost monotone, atriodic, feebly monotone, local homeomorphism, locally confluent, locally weakly confluent, strongly monotone and weakly semi-confluent.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2016.09.011