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On Vertical Order of One-Dimensional Compacta in E3

Published online by Cambridge University Press:  20 November 2018

Fred Tinsley  and
David G. Wright
Fred Tinsley
Affiliation:
Colorado College, Colorado Springs, Colorado
David G. Wright
Affiliation:
Brigham Young University, Provo, Utah
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Let X be a compactum in En of dimension at most n – 2. In [9, Theorem 4.1] it was shown that there is an arbitrarily small homeomorphism h of En fixed outside any given neighborhood of X, so that h(X) has vertical order n – 1 provided n ≠ 3. If X is a 0-dimensional set or a tame 1-dimensional set in E3 then the result is still true. However, the examples of tangled continua of Bothe [2] and McMillan and Row [7] are not amenable to the techniques used in dimensions other than three. This prompted Wright [9] to make the following conjecture.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 36 , Issue 3 , 01 June 1984 , pp. 520 - 528
Copyright
Copyright © Canadian Mathematical Society 1984

References

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