Induced mappings on symmetric products of continua

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• 作者：José ; G. Anaya ^{jgao@uaemex.mx" class="auth_mail" title="E-mail the corresponding author} ; Fé ; lix Capulí ; n ^{fcp@uaemex.mx" class="auth_mail" title="E-mail the corresponding author} ; David Maya ; ^{dmayae@outlook.com" class="auth_mail" title="E-mail the corresponding author} ; Fernando Orozco-Zitli ^{forozcozitli@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 54B20 ; 54C10 ; secondary ; 54F15
• 刊名：Topology and its Applications
• 出版年：2016
• 出版时间：1 December 2016
• 年：2016
• 卷：214
• 期：Complete
• 页码：100-108
• 全文大小：345 K

文摘

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