A brief proof of Cauchy’s integral theorem
نویسندگان
چکیده
منابع مشابه
Another proof of Banaschewski's surjection theorem
We present a new proof of Banaschewski's theorem stating that the completion lift of a uniform surjection is a surjection. The new procedure allows to extend the fact (and, similarly, the related theorem on closed uniform sublocales of complete uniform frames) to quasi-uniformities ("not necessarily symmetric uniformities"). Further, we show how a (regular) Cauchy point on a closed uniform subl...
متن کاملProof of Theorem A
Since the full proof of this theorem 10] is simple yet quite tedious, we connne ourselves to the guidelines of the proof. Observing the angles between the three sample points s i ; s j ; s k forming the minimal angle and the corresponding VD vertex v, we take advantage of the fact that d(v; s i) < d(s i ; s k) (Theorem 4.2(ii)) and, by trigonometric arguments, show that sin sin(120) R M
متن کاملA new proof for the Banach-Zarecki theorem: A light on integrability and continuity
To demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the Banach-Zareckitheorem is presented on the basis of the Radon-Nikodym theoremwhich emphasizes on measure-type properties of the Lebesgueintegral. The Banach-Zarecki theorem says that a real-valuedfunction $F$ is absolutely continuous on a finite closed intervalif and only if it is continuo...
متن کاملA Brief Proof of a Maximal Rank Theorem for Generic Double Points in Projective Space
We give a simple proof of the following theorem of J. Alexander and A. Hirschowitz: Given a general set of points in projective space, the homogeneous ideal of polynomials that are singular at these points has the expected dimension in each degree of 4 and higher, except in 3 cases.
متن کاملA proof of Kummer’s theorem
Following suggestions of T. H. Koornwinder [3], we give a new proof of Kummer’s theorem involving Zeilberger’s algorithm, the WZ method and asymptotic estimates. In the first section, we recall a classical proof given by L. J. Slater [7]. The second section discusses the new proof, in the third section sketches of similar proofs for Bailey’s and Dixon’s theorems are given. The author is gratefu...
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: 1971
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1971-0277699-8