Michal, A. D. (1940) Differentials of Functions with Arguments and Values in Topological Abelian Groups. Proceedings of the National Academy of Sciences of the United States of America, 26 (5). pp. 356-359. ISSN 0027-8424. PMCID PMC1078188. https://resolver.caltech.edu/CaltechAUTHORS:20150811-112829955
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Abstract
By a topological abelian group T (t.a.g. T) we shall mean an abstract abelian group-written additively-such that (a) the function x + y and the inverse function -x are continuous functions (neighborhood continuity) of both variables x and y and of the variable x, respectively, with respect to a postulated Hausdorff topology; (b) given any y ε T and any Hausdorff neighborhood U of 0 ε T, there exists a "positive integer" n such that y ε nU. In this note we shall give brief indications of a differential calculus for functions f(x) with x e t.a.g. T_1 and values in a t.a.g. T_2. Proofs and further developments will appear elsewhere.
Item Type: | Article | |||||||||
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Additional Information: | © 1940 National Academy of Sciences. Communicated April 15, 1940. | |||||||||
Issue or Number: | 5 | |||||||||
PubMed Central ID: | PMC1078188 | |||||||||
Record Number: | CaltechAUTHORS:20150811-112829955 | |||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20150811-112829955 | |||||||||
Official Citation: | Differentials of Functions with Arguments and Values in Topological Abelian Groups A. D. Michal PNAS 1940 26 (5) 356-359 | |||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
ID Code: | 59408 | |||||||||
Collection: | CaltechAUTHORS | |||||||||
Deposited By: | George Porter | |||||||||
Deposited On: | 11 Aug 2015 20:52 | |||||||||
Last Modified: | 03 Oct 2019 08:46 |
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