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Rigid Continua With Many Embeddings

Published online by Cambridge University Press:  20 November 2018

Jun Terasawa
Jun Terasawa*
Affiliation:
Department of Mathematics The National Defense Academy Yokosuka 239, Japan
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Abstract

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A separable metric space X is called rigid if the identity 1X is the only autohomeomorphism, and homogeneous if, for any points x, y of X, there is an (onto) homeomorphism h: X → X such that h(x) = y.

In this note, we show that this onto-ness of the homeomorphism h could not be removed in the definition of homogeneity, by constructing a continuum X which is rigid and has many embeddings, that is, for any two points x, y, there is an embedding (= into homeomorphism) h: X→X such that h(x) = y.

Keywords

54F2054G15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 4 , 01 December 1992 , pp. 557 - 559
Copyright
Copyright © Canadian Mathematical Society 1992

References

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3. Terasawa, J., A rigid space with many embeddings, Indagationes Math. 49(1987), 469–472.Google Scholar