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Lipschitz retractions on symmetric products of trees

Author

Listed:
  • 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)

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 .

Suggested Citation

  • Enrique Castañeda-Alvarado & Fernando Orozco-Zitli & Mónica A. Reyes-Quiroz, 2021. "Lipschitz retractions on symmetric products of trees," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(4), pages 1072-1084, December.
    • Handle: RePEc:spr:indpam:v:52:y:2021:i:4:d:10.1007_s13226-021-00045-4
    DOI: 10.1007/s13226-021-00045-4
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