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Homogeneous Continua Which are Almost Chainable1

Published online by Cambridge University Press:  20 November 2018

C. E. Burgess
C. E. Burgess*
Affiliation:
University of Utah
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The only known examples of nondegenerate homogeneous plane continua are the simple closed curve, the circle of pseudo-arcs (6), and the pseudo-arc (1; 13). Another example, called the pseudo-circle, has been suggested by Bing (2), but it has not been proved to be homogeneous. (Definitions of some of these terms and a history of results on homogeneous plane continua can be found in (6).) Of the three known examples, the pseudo-arc is both linearly chainable and circularly chainable, and the simple closed curve and the circle of pseudo-arcs are circularly chainable but not linearly chainable. It is not known whether every homogeneous plane continuum is either linearly chainable or circularly chainable. Bing has shown that a homogeneous continuum is a pseudo-arc provided it is linearly chainable (4).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 13 , 1961 , pp. 519 - 528
Copyright
Copyright © Canadian Mathematical Society 1961

References

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