Tame Arcs on Disks
نویسنده
چکیده
It is the goal of this note to show that each disk in E3 contains a tame arc which intersects the boundary of D. In [l ] Bing shows that each disk in E3 contains many tame arcs. The reason that the arguments given in [l ] do not show that each disk contains a tame arc intersecting the boundary is that a disk in E3 need not lie on a closed surface in E3 [7]. This difficulty can be overcome using Bing's improvement of the "side approximation theorem" [2] and a theorem of Hempel [6], Suppose that D is a disk in E3.
منابع مشابه
A Fundamental Theorem on Decompositions of the Sphere into Points and Tame Arcs
1. Introduction. R. H. Bing showed that an upper semicontinuous decomposition of £3 into points and tame arcs did not necessarily produce a decomposition space topologically equivalent to E3 [1J. M. L. Curtis and R. L. Wilder showed [2] that the decomposition space of Bing was a homotopy manifold, thus negatively answering a question proposed by Griffiths [3J. R. Rosen recently announced [4] a ...
متن کاملA Note on Piercing a Disk
In this note we give a sufficient condition that a 2-cell or disk in E3 be pierced by a tame arc at each point of its interior. This condition is simply that each arc in the disk be tame. The method of proof leans heavily upon some results of Bing and Moise as well as upon a theorem on the union of tame disks by one of the present authors. Remark. Lemma 7 of [2] asserts that if two tame disks i...
متن کاملRandom Arc Allocation and Applications to Disks, Drums and DRAMs
The paper considers a generalization of the well known random placement of balls into bins. Given n circular arcs of lengths αi, 0 i< n we study the maximum number of overlapping arcs on a circle if the starting points of the arcs are chosen randomly. We give bounds that are tight up to constant factors in the lower order terms using a technique that combines Chernoff bounds with random walks. ...
متن کاملRandom Arc Allocation and Applications
The paper considers a generalization of the well known random placement of balls into bins. Given n circular arcs of lengths 1, : : : ,n we study the maximum number of overlapping arcs on a circle if the starting points of the arcs are chosen randomly. We give almost exact tail bounds on the maximum overlap of the arcs. These tail bounds yield a characterization of the expected maximum overlap ...
متن کاملTail Bounds And Expectations For Random Arc Allocation And Applications
The paper considers a generalization of the well known random placement of balls into bins. Given n circular arcs of lengths αi, 0 i n we study the maximum number of overlapping arcs on a circle if the starting points of the arcs are chosen randomly. We give almost exact tail bounds on the maximum overlap of the arcs. These tail bounds yield a complete characterization of the expected maximum o...
متن کامل