Continuous homomorphisms are differentiable
نویسندگان
چکیده
منابع مشابه
Everywhere Continuous Nowhere Differentiable Functions
Here I discuss the use of everywhere continuous nowhere differentiable functions, as well as the proof of an example of such a function. First, I will explain why the existence of such functions is not intuitive, thus providing significance to the construction and explanation of these functions. Then, I will provide a specific detailed example along with the proof for why it meets the requireme...
متن کاملThe Set of Continuous Nowhere Differentiable Functions
Let C be the space of all real-valued continuous functions defined on the unit interval provided with the uniform norm. In the Scottish Book, Banach raised the question of the descriptive class of the subset D of C consisting of all functions which are differentiable at each point of [0,1]. Banach pointed out that D forms a coanalytic subset of C and asked whether D is a Borel set. Later Mazurk...
متن کاملThe Prevalence of Continuous Nowhere Differentiable Functions
In the space of continuous functions of a real variable, the set of nowhere dilferentiable functions has long been known to be topologically "generic". In this paper it is shown further that in a measure theoretic sense (which is different from Wiener measure), "almost every" continuous function is nowhere dilferentiable. Similar results concerning other types of regularity, such as Holder cont...
متن کاملContinuous Homomorphisms on βN and Ramsey Theory
We consider the question of the existence of a nontrivial continuous homomorphism from (βN,+) into N∗ = βN\N. This problem is known to be equivalent to the existence of distinct p and q in N∗ satisfying the equations p+ p = q = q + q = q + p = p+ q. We obtain certain restrictions on possible values of p and q in these equations and show that the existence of such p and q implies the existence o...
متن کاملA note on continuous behavior homomorphisms
The purpose of this note is the characterization of the class of behavior homomorphisms that have nice polynomial representations. The key to this is a judicious application of duality theory together with additional continuity requirements. c © 2003 Elsevier B.V. All rights reserved.
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 American Mathematical Society
سال: 1977
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1977-0455016-3