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Homomorphisms of Continuous Pseudogroups

Published online by Cambridge University Press:  22 January 2016

Joseph E. D’atri
Joseph E. D’atri*
Affiliation:
Rutgers, The State University of New JerseyNew Brunswick, New Jersey
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In this paper we attempt to set up a notion of homomorphism for continuous pseudogroups and show that the kernel exists (as a continuous pseudogroup) in the transitive case. This paper is really an extension of the paper by Kuranishi and Rodrigues [11] which essentially examines the question of the existence (as a continuous pseudogroup) of an image of a homomorphism. A certain amount of overlap in definitions and statements of results was unavoidable, especially in sections 2 and 3, but for many proofs and constructions the reader is referred to that paper. For the basic notions of the theory of continuous pseudogroups as used in section 4, see Kuranishi [9] and for the terminology of the Cartan-Kãhler theory used in section 5, see Kuranishi [6] Fuller expositions may be found in Cartan [I] Kàhler [4], Kumpera [5], Kuranishi [7], and Schouten and v.d. Kulk [13].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 25 , 1965 , pp. 143 - 163
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1965

References

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