منابع مشابه
Concerning Connected and Regular Point Sets
In this paper an extension will be given of a theorem of the author'sf which states that if A and B are any two points of a continuous curve M, and K denotes the set of all those points of M which separate} A and B in M, then K+A+B is a closed set of points. I t will be shown that if A and B are any two points of any connected and regular (connected im kleinen) point set M, and K denotes the se...
متن کاملApplications of a Theorem concerning Sets with Connected Sections
As the reader can notice, the title of the present paper differs from that of [3] only because the term connected replaces the term convex. This is not casual. Indeed, it remains our aim to show, by means of a series of further applications, the usefulness of our recent Theorem 2.3 of [6] which, in a certain sense, can be regarded as a “connected” version of the famous Theorems 1′ and 2 of [3]....
متن کاملA Theorem concerning Closed and Compact Point Sets Which Lie in Connected Domains
PROOF. For each point P of D, there exists a region gp of Gi containing P such that gp is a subset of D. By Axiom 2, there exists a connected domain dp containing P which is a subset of gp. Let Ui denote the collection of all domains dp for each point P of D. The point set M is closed and compact, and hence, by Theorem 22 of Chapter I, it is covered by a finite subcollection W\ of U\. By Theore...
متن کاملFour-connected triangulations of planar point sets
In this paper, we consider the problem of determining in polynomial time whether a given planar point set P of n points admits 4-connected triangulation. We propose a necessary and sufficient condition for recognizing P , and present an O(n) algorithm of constructing a 4-connected triangulation of P . Thus, our algorithm solves a longstanding open problem in computational geometry and geometric...
متن کاملConnected Rectilinear Graphs on Point Sets
Let V be a set of n points in R. We study the question whether there exists an orientation such that V is the vertex set of a connected rectilinear graph in that orientation. A graph is rectilinear if its edges are straight line segments in d pairwise perpendicular directions. We prove that at most one such orientation can be possible, up to trivial rotations of 90◦ around some axis. In additio...
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: Fundamenta Mathematicae
سال: 1922
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-3-1-238-239