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Currently displaying 1 – 3 of 3

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Symmetric products of the Euclidean spaces and the spheres

Naotsugu Chinen — 2015

Commentationes Mathematicae Universitatis Carolinae

By $F_{n} (X)$ , $n \geq 1$ , we denote the $n$ -th symmetric product of a metric space $(X, d)$ as the space of the non-empty finite subsets of $X$ with at most $n$ elements endowed with the Hausdorff metric $d_{H}$ . In this paper we shall describe that every isometry from the $n$ -th symmetric product $F_{n} (X)$ into itself is induced by some isometry from $X$ into itself, where $X$ is either the Euclidean space or the sphere with the usual metrics. Moreover, we study the $n$ -th symmetric product of the Euclidean space up to bi-Lipschitz equivalence and...

Perfectness of the Higson and Smirnov compactifications

Yuji Akaike; Naotsugu Chinen; Kazuo Tomoyasu — 2007

Colloquium Mathematicae

We provide a necessary and sufficient condition for the Higson compactification to be perfect for the noncompact, locally connected, proper metric spaces. We also discuss perfectness of the Smirnov compactification.

Colorings of Periodic Homeomorphisms

Yuji Akaike; Naotsugu Chinen; Kazuo Tomoyasu — 2009

Bulletin of the Polish Academy of Sciences. Mathematics

We calculate the exact value of the color number of a periodic homeomorphism without fixed points on a finite connected graph.

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