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Differentials of Functions with Arguments and Values in Topological Abelian Groups

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
Related URLs:
URLURL TypeDescription
http://www.pnas.org/content/26/5/356.full.pdfPublisherArticle
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1078188/PubMed CentralArticle
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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