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...
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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...
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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.
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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 ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1993
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1993-1146867-x