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Algebraic Approximation of Curves

Published online by Cambridge University Press:  20 November 2018

A. H. Wallace
A. H. Wallace*
Affiliation:
University of Toronto
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In his paper on the algebraic approximation of differentiable manifolds Nash (1) introduced the concept of a sheet of a real algebraic variety (see the definition in §16 below) and raised certain questions of a general nature. In attempting to answer these questions it has been necessary to evolve some sort of technique for manipulating curves on algebraic varieties, and, in particular, to set up a criterion for the possibility of approximating a sequence of analytic arcs (definition in §1) joined end to end by a single analytic arc.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 10 , 1958 , pp. 242 - 278
Copyright
Copyright © Canadian Mathematical Society 1958

References

1. J. Nash, , Real algebraic manifolds, Ann. of Math., 56 (1952), 405-421.Google Scholar
2. P. Samuel, , Sur l'algébricité de certains points singuliers, J. de Math, pures et appl. (9), 35 (1956), 1-6.Google Scholar
3. A. H. Wallace, , Algebraic approximation of manifolds, Proc. London Math. Soc. (3), 7 (1957), 196-210.Google Scholar
4. H. Whitney, , Elementary structure of real algebraic varieties, Ann. of Math., 66 (1957), 545- 556.Google Scholar