A proof of the most general polyhedral Schoenflies conjecture possible
نویسندگان
چکیده
منابع مشابه
On the Combinatorial Schoenflies Conjecture
Introduction. The combinatorial version of the Schoenflies conjecture in dimension n states: A combinatorial (n — l)-sphere on a combinatorial «-sphere decomposes the latter into two combinatorial ncells. The cases n = 1, 2 are obvious, the case n = 3 was solved by J. W. Alexander [l], see also W. Graeub [5], and E. Moise [8]. Nothing is known for n>3 (compare J. F. Hudson and E. C. Zeeman in [...
متن کاملThe Five Dimensional Polyhedral Schoenflies Theorem
Introduction. The central result of this note is a proof that in the 5-sphere with its usual piecewise linear structure, a subpolyhedron homeomorphic to 5 4 bounds two topological 5-cells. Some related facts about imbeddings of 5 n 1 in S are also included. Our information about such imbeddings is quite incomplete, so it may be appropriate, after making a few definitions, to summarize current k...
متن کاملProof for a Conjecture on General Means
We give a proof for a conjecture suggested by Olivier de La Grandville and Robert M. Solow, which says that the general mean of two positive numbers, as a function of its order, has one and only one inflection point.
متن کاملProof of the Most Informative Boolean Function Conjecture
Suppose X is a uniformly distributed N -dimensional binary vector and Y is obtained by passing X through a binary symmetric channel with crossover probability α. Recently, Courtade and Kumar postulates that I(f(X);Y) ≤ 1−Hb(α) for any Boolean function f [1]. In this paper, we provide a proof of the correctness of this conjecture. I. PROBLEM STATEMENT Let X be an N -dimensional binary random vec...
متن کاملA short proof of the maximum conjecture in CR dimension one
In this paper and by means of the extant results in the Tanaka theory, we present a very short proof in the specific case of CR dimension one for Beloshapka's maximum conjecture. Accordingly, we prove that each totally nondegenerate model of CR dimension one and length >= 3 has rigidity. As a result, we observe that the group of CR automorphisms associated with each of such models contains onl...
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: Pacific Journal of Mathematics
سال: 1971
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1971.38.401