Mappings of indecomposable continua
نویسندگان
چکیده
منابع مشابه
Certain Homogeneous Unicoherent Indecomposable Continua
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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In this paper we prove the existence of uncountably many indecomposable continua in the dynamics of complex exponentials of the form Eλ(z) = λe z with λ > 1/e. These continua contain points that share the same itinerary under iteration of Eλ. These itineraries are bounded but consist of blocks of 0’s whose lengths increase, and hence these continua are never periodic.
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Various kinds of nonseparating subcontinua were studied by a number of authors, see, for example, the expository paper [2], where a large amount of information on this subject is given. In the topological literature, or in continuum theory (to be more precise), the term “terminal,” when applied either to subcontinua of a given continuum or to points, and the same name “terminal” was assigned to...
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Swingle [7]1 has given the following definitions. (1) A continuum M is said to be the finished sum of the continua of a collection G if G* = M and no continuum of G is a subset of the sum of the others.2 (2) If » is a positive integer, the continuum M is said to be indecomposable under index » if If is the finished sum of « continua and is not the finished sum of »+1 continua. Swingle has shown...
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Let X be a Hausdorff continuum (a compact connected Hausdorff space). Let 2X (respectively, Cn(X)) denote the hyperspace of nonempty closed subsets of X (respectively, nonempty closed subsets of X with at most n components), with the Vietoris topology. We prove that if X is hereditarily indecomposable, Y is a Hausdorff continuum and 2X (respectively Cn(X)) is homeomorphic to 2Y (respectively, C...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1971
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1971-0287513-2