Homogeneous, separating plane continua are decomposable.
نویسندگان
چکیده
منابع مشابه
A Complete Classification of Homogeneous Plane Continua
We show that the only compact and connected subsets (i.e. continua) X of the plane R2 which contain more than one point and are homogeneous, in the sense that the group of homeomorphisms of X acts transitively on X, are, up to homeomorphism, the circle S1, the pseudo-arc, and the circle of pseudo-arcs. These latter two spaces are fractal-like objects which do not contain any arcs. It follows th...
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Let X be a plane separating continuum. Suppose C is a convex space contained in a bounded component of R2 − X. It is shown that the span of the boundary of C is a lower bound for both the span and semispan of X. It is also shown that if a span of X is equal to the breadth of X and Y satisfies certain conditions relative to X then that span of X is an upper bound for the corresponding span of Y .
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A simple closed curve is the simplest example of a compact, nondegenerate, homogeneous continuum. If a bounded, nondegenerate, homogeneous plane continuum has any local connectedness property, even of the weakest sort, it is known to be a simple closed curve [l, 2, 3].1 The recent discovery of a bounded, nondegenerate, homogenous plane continuum which does not separate the plane [4, 5] has give...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 1981
ISSN: 0026-2285
DOI: 10.1307/mmj/1029002562