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Sequential decreasing strong size properties

In: Mathematica Slovaca, vol. 68, no. 5
Félix Capulín - Miguel A. Lara - Fernando Orozco-Zitli
Detaily:
Rok, strany: 2018, 1141 - 1148
Kľúčové slová:
$n$-fold hyperspace, strong size property, strong size map, Kelley continuum, indecomposability, local connectedness, continuum chainability and unicoherence
O článku:
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 $\mathcal{P}$ 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 $\lim tj= t\in[0,1)$ $(t\in(0,1))$ and each fiber $μ-1 (tj)$ has property $\mathcal{P}$, 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.
Ako citovať:
ISO 690:
Capulín, F., Lara, M., Orozco-Zitli, F. 2018. Sequential decreasing strong size properties. In Mathematica Slovaca, vol. 68, no.5, pp. 1141-1148. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0176

APA:
Capulín, F., Lara, M., Orozco-Zitli, F. (2018). Sequential decreasing strong size properties. Mathematica Slovaca, 68(5), 1141-1148. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0176
O vydaní:
Publikované: 31. 10. 2018