Peano Continua with Unique Symmetric Products

Autor:	David Herrera-Carrasco, Fernando Macías-Romero, Francisco Vazquez-Juarez
Rok vydání:	2012
Předmět:	Combinatorics Mathematics::Group Theory Hyperspace Hausdorff distance Integer Continuum (topology) Peano axioms Mathematical analysis Metric (mathematics) Mathematics::General Topology Mathematics
Zdroj:	Journal of Mathematics Research. 4
ISSN:	1916-9809 1916-9795
DOI:	10.5539/jmr.v4n4p1
Popis:	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 $n\geq 4.$ Our result generalize all the previous known results on this subject.
Databáze:	OpenAIRE
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