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On the presentation of stratified sets and singular varieties

Part of: General theory of differentiable manifolds

Published online by Cambridge University Press:  26 February 2010

F. E. A. Johnson
F. E. A. Johnson
Affiliation:
Department of Mathematics, University College London, Gower Street, London. WC1E 6BT
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Extract

The aim of this paper is to give a clear statement, and, I hope, a reasonably clear proof, of a theorem of Thorn, which occurs in his important and difficult paper “Ensembles et morphismes stratifiés” [10]. The theorem to which I refer is Théorème 1.D.1 of [10]. “Tout espace stratifié compact admet une présentation associée aux applications kYX données”. At least, I think that the theorem herein described is equivalent to the above, but I could not swear to it. The main difficulty is that, despite strenuous efforts on my part, I have always found it easier to rig up my own system of definitions than to work within the framework suggested by Thorn. However, the two accounts clearly say the same sort of thing. In particular, §1 of the present paper is closely related to, and heavily influenced by, the material on page 250 of [10].

MSC classification

Secondary: 58A35: Stratified sets
Type
Research Article
Information
Mathematika , Volume 29 , Issue 1 , June 1982 , pp. 135 - 170
Copyright
Copyright © University College London 1982

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References

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