Convexification of Locally Connected Generalized Continua
نویسندگان
چکیده
منابع مشابه
On generalized homogeneity of locally connected plane continua
The well-known result of S. Mazurkiewicz that the simple closed curve is the only nondegenerate locally connected plane homogeneous continuum is extended to generalized homogeneity with respect to some other classes of mappings. Several open problems in the area are posed.
متن کاملEnds of Cusp-Uniform Groups of Locally Connected Continua - I
Due to works by Bestvina-Mess, Swarup and Bowditch, we now have complete knowledge of how splittings of a word-hyperbolic group G as a graph of groups with finite or two-ended edge groups relate to the cut point structure of its boundary. It is central in the theory that ∂G is a locally connected continuum (a Peano space). Motivated by the structure of tight circle packings, we propose to gener...
متن کاملOn Non-cut Sets of Locally Connected Continua
W. L. Ayres and H. M. Gehman have proved independently that if a locally connected continuum S contains a non-cut point p, there exists an arbitrarily small region R containing p and such that S — R is connected. Our paper is concerned with certain generalizations of this theorem. We shall consider a space 5 which is a locally connected continuum and contains a closed set P such that S — P is c...
متن کاملMore Monotone Open Homogeneous Locally Connected Plane Continua
This paper constructs a continuous decomposition of the Sierpiński curve into acyclic continua one of which is an arc. This decomposition is then used to construct another continuous decomposition of the Sierpiński curve. The resulting decomposition space is homeomorphic to the continuum obtained from taking the Sierpiński curve and identifying two points on the boundary of one of its complemen...
متن کاملIncomputability of Simply Connected Planar Continua
Le Roux and Ziegler asked whether every simply connected compact nonempty planar Π 1 set always contains a computable point. In this paper, we solve the problem of le Roux and Ziegler by showing that there exists a planar Π 1 dendroid without computable points. We also provide several pathological examples of tree-like Π 1 continua fulfilling certain global incomputability properties: there is ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Hiroshima Mathematical Journal
سال: 1955
ISSN: 0018-2079
DOI: 10.32917/hmj/1556071223