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On Almost Regular Homeomorphisms

Published online by Cambridge University Press:  20 November 2018

S. K. Kaul
S. K. Kaul*
Affiliation:
University of Calgary, Calgary, Alberta
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Let (X, d) be a metric space with metric d, and h be a homeomorphism of X onto itself. Any point y in X is called a regular point (2) under A if for any given ϵ > 0 there exists a δ > 0 such that d(x, y) < δ implies that d(hn(x), hn(y)) < ϵ for all integers n, where hn is the composition of h or h-1 with itself |n| times, depending upon whether n is positive or negative, and h0 is the identity on X. If y is not regular under h, then y is called irregular. We shall denote the set of regular points by R(h) and the set of irregular points by I(h).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1 - 6
Copyright
Copyright © Canadian Mathematical Society 1968

References

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