On the metric dimension of converging sequences

Ladislav, Jr. Mišík; Tibor Žáčik

Displaying similar documents to “On the metric dimension of converging sequences”

On some properties of the metric dimension

Ladislav Mišík, Tibor Žáčik (1990)

Commentationes Mathematicae Universitatis Carolinae

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Two theorems for the $n$ -dimensionality of metric spaces

Jun-Iti Nagata (1962-1964)

Compositio Mathematica

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A geometric proof to Cantor's theorem and an irrationality measure for some Cantor's series.

Marques, Diego (2008)

Annales Mathematicae et Informaticae

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On character of points in the Higson corona of a metric space

Taras O. Banakh, Ostap Chervak, Lubomyr Zdomskyy (2013)

Commentationes Mathematicae Universitatis Carolinae

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We prove that for an unbounded metric space $X$ , the minimal character $𝗆 χ (\overset{ˇ}{X})$ of a point of the Higson corona $\overset{ˇ}{X}$ of $X$ is equal to $𝔲$ if $X$ has asymptotically isolated balls and to $max {𝔲, 𝔡}$ otherwise. This implies that under $𝔲 < 𝔡$ a metric space $X$ of bounded geometry is coarsely equivalent to the Cantor macro-cube $2^{< ℕ}$ if and only if $dim (\overset{ˇ}{X}) = 0$ and $𝗆 χ (\overset{ˇ}{X}) = 𝔡$ . This contrasts with a result of Protasov saying that under CH the coronas of any two asymptotically zero-dimensional unbounded metric separable spaces are homeomorphic. ...

Displaying similar documents to “On the metric dimension of converging sequences”

On some properties of the metric dimension

Two theorems for the n -dimensionality of metric spaces

A geometric proof to Cantor's theorem and an irrationality measure for some Cantor's series.

On character of points in the Higson corona of a metric space

Two theorems for the $n$ -dimensionality of metric spaces