Non-Confluence of the Natural Map of Products onto Symmetric Products

Martínez-Montejano, Jorge M.

doi:10.1201/9780203910245.ch16

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“…Since X is locally connected, Y is also locally connected. By [8, Theorem 1.1 (19)], dim(X) = 1. Thus dim(F n (Y )) = dim(F n (X)) = n. Assume that dim(Y ) > 1.…”

Section: The Main Theoremmentioning

confidence: 99%

Dendrites and symmetric products

Acosta¹,

Hernández-Gutiérrez²,

Martı́nez-de-la-Vega³

2009

Glas. Mat. Ser. III

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Abstract. For a given continuum X and a natural number n, we consider the hyperspace Fn(X) of all nonempty subsets of X with at most n points, metrized by the Hausdorff metric. In this paper we show that if X is a dendrite whose set of end points is closed, n ∈ N and Y is a continuum such that the hyperspaces Fn(X) and Fn(Y ) are homeomorphic, then Y is a dendrite whose set of end points is closed.

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“…Since X is locally connected, Y is also locally connected. By [8, Theorem 1.1 (19)], dim(X) = 1. Thus dim(F n (Y )) = dim(F n (X)) = n. Assume that dim(Y ) > 1.…”

Section: The Main Theoremmentioning

confidence: 99%

Dendrites and symmetric products

Acosta¹,

Hernández-Gutiérrez²,

Martı́nez-de-la-Vega³

2009

Glas. Mat. Ser. III

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Induced mappings between quotient spaces of symmetric products of continua

Castañeda-Alvarado

Orozco-Zitli

Sánchez–Martínez

2014

Topology and its Applications

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Peano Continua with Unique Symmetric Products

Herrera-Carrasco¹,

Macías-Romero²,

Vazquez-Juarez³

2012

JMR

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Let $X$ be a metric continuum and $n$ a positive integer. Let $F_{n}(X)$ be the hyperspace of all nonempty subsets of $X$ with at most $n$ points, metrized by the Hausdorff metric. We said that $X$ has unique hyperspace $F_n(X)$ provided that, if $Y$ is a continuum and $F_n(X)$ is homeomorphic to $F_n(Y),$ then $X$ is homeomorphic to $Y.$ In this paper we study Peano continua $X$ that have unique hyperspace $F_n(X)$, for each $ngeq 4.$ Our result generalize all the previous known results on this subject

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Non-Confluence of the Natural Map of Products onto Symmetric Products

Cited by 3 publications

References 0 publications

Dendrites and symmetric products

Dendrites and symmetric products

Induced mappings between quotient spaces of symmetric products of continua

Peano Continua with Unique Symmetric Products

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