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Mathematica Slovaca

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Volume 68, Issue 5

Issues

Sequential decreasing strong size properties

Féelix Capulín
  • Facultad de Ciencias Campus Universitario El Cerrillo Universidad Autónoma del Estado de México Piedras Blancas, Toluca Estado de México C.P. 50200 México
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/ Miguel A. Lara
  • Facultad de Ciencias Campus Universitario El Cerrillo Universidad Autónoma del Estado de México Piedras Blancas, Toluca Estado de México C.P. 50200 México
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/ Fernando Orozco-Zitli
  • Facultad de Ciencias Campus Universitario El Cerrillo Universidad Autónoma del Estado de México Piedras Blancas, Toluca Estado de México C.P. 50200 México
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Published Online: 2018-10-20 | DOI: https://doi.org/10.1515/ms-2017-0176

Abstract

Let X be a continuum. The n-fold hyperspace Cn(X), n < ∞, is the space of all nonempty closed subsets of X with at most n components. A topological property P is said to be a (an almost) sequential decreasing strong size property provided that if μ is a strong size map for Cn(X, {tj}j=1 is a sequence in the interval (t,1) such that lim tj = t ∈ [0,1) (t ∈ (0,1)) and each fiber μ−1(tj) has property P, then so does μ−1(t). In this paper we show that the following properties are sequential decreasing strong size properties: being a Kelley continuum, local connectedness, continuum chainability and, unicoherence. Also we prove that indecomposability is an almost sequential decreasing strong size property.

MSC 2010: Primary 54C05, 54C10, 54B20; Secondary 54B15

Keywords: n-fold hyperspace; strong size property; strong size map; Kelley continuum; indecomposability; local connectedness; continuum chainability and unicoherence

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About the article

Received: 2016-10-14

Accepted: 2017-09-01

Published Online: 2018-10-20

Published in Print: 2018-10-25


Communicated by David Buhagiar


Citation Information: Mathematica Slovaca, Volume 68, Issue 5, Pages 1141–1148, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0176.

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