A Steinhaus type theorem
نویسندگان
چکیده
منابع مشابه
A two dimensional Steinhaus theorem
In 1958 this was proved independently by S. Swierczkowski [15] and by P. Erdos and V.T. Sos [12],[13]. It is often called the Steinhaus theorem or Steinhaus Conjecture. A useful way of viewing the result is to think of a circle of unit circumference with points placed around the perimeter at distances 0, 0:, ... , (N 1)0: from an arbitrary origin on the perimeter. Then the distances between adj...
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We deal with the distribution of N points placed consecutively around the circle by a fixed angle of α. From the proof of Tony van Ravenstein [RAV88], we propose a detailed proof of the Steinhaus conjecture whose result is the following: the N points partition the circle into gaps of at most three different lengths. We study the mathematical notions required for the proof of this theorem reveal...
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The space D(R) of test functions (infinitely differentiable functions with compact support) is an important example of a non-metrizable (LF)-space, and the domain of distributions (generalized functions). E. Bishop suggested in [1, Appendix A] and [2, Chapter 7, Notes] that the completeness of D(R) and the weak completeness of its dual space would not hold in Bishop’s constructive mathematics. ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1987
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1987-0875397-2