Concerning indecomposable continua and upper semicontinuous collections of nondegenerate 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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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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In this paper propositions will be established concerning the collection of all the cut points of a given planef continuum. It will be shown that there does not exist an uncountable collection of mutually exclusive subcontinua of a given continuum M each of which contains at least one cut point of M. With the aid of this fundamental theorem it is shown, among other things, that the set of all t...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1972
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-74-1-35-42