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Concerning Non-Planar Circle-Like Continua

Published online by Cambridge University Press:  20 November 2018

W. T. Ingram
W. T. Ingram*
Affiliation:
Auburn University and The University of Houston
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In this paper it is proved that if a circle-like continuum M cannot be embedded in the plane, then M is not a continuous image of any plane continuum (Theorem 5).

Suppose that (S, ρ) is a metric space. A finite sequence of domains L1, L2, … , Ln is called a linear chain provided Li intersects Lj if and only if |i — j| ⩽ 1. If, in addition, there is a positive number ∊ such that, for each i, the diameter of Li is less than ∊, then the linear chain is called a linear ∊-chain. If for each positive number ∊ the continuum M can be covered by a linear ∊-chain, then M is said to be chainable (or snake-like) (2).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 242 - 250
Copyright
Copyright © Canadian Mathematical Society 1967

References

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