## Differential Topology with a View to Applications |

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### Contents

Basic topological ideas | 1 |

Calculus | 36 |

Remarks on the literature | 115 |

Copyright | |

5 other sections not shown

### Common terms and phrases

apply atlas Banach space behaviour bifurcation theory bijection bounded called catastrophe charts closed co-ordinates compact condition consider contains continuous convert corresponding critical points defined definition denote derivative Df(x diffeomorphism differentiable dimensions discussion dynamical systems easy element equations equivalent euclidean example exists fact Figure finite fixed points flow follows function germ given gives global homeomorphism hyperbolic idea implies important infinite interval inverse isomorphism linear map locally look manifold matrix Mean Value Theorem means metric spaces natural neighbourhood normed linear space Note Observe obtain open sets origin particular possible precisely proof prove Remarks representatives respectively result Rule satisfies scalar sense shows singular smooth solution stable structure submanifold suppose tangent theorem theory topological space topology usual vector field write