On uniquely arcwise connected curves
نویسندگان
چکیده
منابع مشابه
Colouring Arcwise Connected Sets in the Plane II
Let G be the family of nite collections S where S is a collection of closed, bounded, arcwise connected sets in R 2 which for any S; T 2 S where S \ T 6 = ;, it holds that S \ T is arcwise connected. Given S 2 G which is triangle-free, we show that provided S is suu-ciently large there exists a subcollection S 0 S of at most 5 sets with the property that the sets of S surrounded by S 0 induce a...
متن کاملArcwise Connectedness of the Boundaries of Connected Self-similar Sets
Let T be the attractor of injective contractions f1, . . . , fm on R 2 that satisfy the Open Set Condition. If T is connected, ∂T is arcwise connected. In particular, the boundary of the Lévy dragon is arcwise connected.
متن کاملColouring Arcwise Connected Sets in the Plane I
Let G be the family of ®nite collections S where S is a collection of bounded, arcwise connected sets in R which for any S;T A S where S VT 0h, it holds that S VT is arcwise connected. We investigate the problem of bounding the chromatic number of the intersection graph G of a collection S A G. Assuming G is triangle-free, suppose there exists a closed Jordan curve C HR such that C intersects a...
متن کاملAre scattering properties of graphs uniquely connected to their shapes?
The famous question of Kac "can one hear the shape of a drum?" addressing the unique connection between the shape of a planar region and the spectrum of the corresponding Laplace operator, can be legitimately extended to scattering systems. In the modified version, one asks whether the geometry of a vibrating system can be determined by scattering experiments. We present the first experimental ...
متن کامل3-connected Planar Spaces Uniquely Embed in the Sphere
We characterize those locally connected subsets of the sphere that have a unique embedding in the sphere — i.e., those for which every homeomorphism of the subset to itself extends to a homeomorphism of the sphere. This implies that if Ḡ is the closure of an embedding of a 3-connected graph in the sphere such that every 1-way infinite path in G has a unique accumulation point in Ḡ, then Ḡ has a...
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: Colloquium Mathematicum
سال: 1987
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-51-1-227-238