منابع مشابه
On the Banach-Steinhaus Theorem
A Banach-Steinhaus theorem for sets of continuous linear mappings on topological modules which are Baire spaces is proved, and some consequences of it are derived. Mathematics Subject Classification: 46H25, 46S10, 46E10
متن کاملThe Banach-Steinhaus theorem for (LF)-spaces in constructive analysis
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. ...
متن کاملA 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...
متن کاملBanach-Steinhaus theory revisited: Lineability and spaceability
In this paper we study the divergence behavior of linear approximation processes in general Banach spaces. We are interested in the structure of the set of divergence creating functions. The Banach–Steinhaus theory gives some information about this set, however, it cannot be used to answer the question whether this set contains subspaces with linear structure. We give necessary and sufficient c...
متن کاملThe Three Gap Theorem (Steinhaus Conjecture)
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...
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: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1973
ISSN: 0386-2194
DOI: 10.3792/pja/1195519345