Concerning the Spans of Certain Plane Separating Continua
نویسندگان
چکیده
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 .
منابع مشابه
On a Certain Type of Homogeneous Plane Continuum
In 1920 very little was known about the class of homogeneous, bounded continua in the plane. At that time Knaster and Kuratowski [l] raised the question:1 Is every such (nondegenerate) continuum a simple closed curve? Mazurkiewicz [2] showed such a continuum is a simple closed curve if it is locally connected, and I showed this is the case if the continuum is aposyndetic [3]. H. J. Cohen [4] pr...
متن کاملA Fixed Point Theorem for Branched Covering Maps of the Plane
It is known that every homeomorphism of the plane has a fixed point in a non-separating, invariant subcontinuum. Easy examples show that a branched covering map of the plane can be periodic point free. In this paper we show that any branched covering map of the plane of degree with absolute value at most two, which has an invariant, non-separating continuum Y , either has a fixed point in Y , o...
متن کاملContinuous Collections of Decomposable Continua on a Spherical Surface
In this paper a study is made of continuous collections of decomposable continua on a spherical surface. Properties of the decomposition spaces of such collections filling up continua are established, and a characterization of the decomposition spaces of such collections filling up a spherical surface is obtained. The results of the present paper are related to certain results obtained by R. D....
متن کاملRotation Sets and Almost Periodic Sequences
We study the rotational behaviour on minimal sets of torus homeomorphisms and show that the associated rotation sets can be any type of line segments as well as non-convex and even plane-separating continua. This shows that restrictions which hold for rotation set on the whole torus are not valid on minimal sets. The proof uses a construction of rotational horseshoes by Kwapisz to transfer the ...
متن کاملConcerning Aposyndetic and Non-aposyndetic Continua
Introduction. One might judge from the title that I am going to discuss continua. For is not a continuum either aposyndetic or nonaposyndetic? What I intend to do is to consider continua from a certain point of view, and from this point of view continua may be classified in a rough sort of way. This system of classification (and the basic concept upon which it rests) is only in its infancy. Her...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999