Lipschitz retractions on symmetric products of trees

Enrique Castañeda-Alvarado (), Fernando Orozco-Zitli () and Mónica A. Reyes-Quiroz ()
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Enrique Castañeda-Alvarado: Instituto Literario No. 100, Universidad Autónoma del Estado de México
Fernando Orozco-Zitli: Instituto Literario No. 100, Universidad Autónoma del Estado de México
Mónica A. Reyes-Quiroz: Instituto Literario No. 100, Universidad Autónoma del Estado de México

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 4, 1072-1084

Abstract: Abstract Given a continuum X and a positive integer n, $$F_n (X)$$ F n ( X ) denotes the hyperspace of non-empty subsets of X with at most n elements, endowed with the Hausdorff metric. In this article, given X a simple m-od, we prove that $$F_{n-1} (X)$$ F n - 1 ( X ) is a $$(6n + 1)$$ ( 6 n + 1 ) - Lipschitz retract of $$F_n (X)$$ F n ( X ) for every $$n\ge 2$$ n ≥ 2 , and that $$F_{n-1} (X)$$ F n - 1 ( X ) is a 4- Lipschitz retract of $$F_n(X)$$ F n ( X ) for X a tree and $$n=2,3$$ n = 2 , 3 .

Keywords: Symmetric products; Retractions; Lipschitz maps; Trees and m-ods; 54B20; 54C15; 54E40 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13226-021-00045-4

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