Hassler Whitney Collected Papers pp 370-406 | Cite as

# On Singularities of Mappings of Euclidean Spaces. I. Mappings of the Plane Into the Plane

Chapter

## Abstract

Let *f* _{0} be a mapping of an open set *R* in *n*-space *E* ^{ n } into *m*-space *E* ^{ m }. Let us consider, along with *f* _{0}, all mappings *f* which are sufficiently good approximations to *f* _{0}. By the Weierstrass Approximation Theorem, there are such mappings *f* which are analytic; in fact, (see [5], Lemma 6) we may make *f* approximate to *f* _{0} throughout *R* arbitrarily well, and if *f* _{0} is *r*-smooth (i.e., has continuous partial derivatives of orders ≦*r*), *r* finite, we may make corresponding derivatives of *f*approximate to those of *f* _{0}.

## Keywords

Singular Point Critical Point Theory Simple Closed Curve Cusp Point Fold Point
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## Bibliography

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© Birkhäuser Boston 1992