Abstract
Differential topology is the study of differentiable manifolds and maps. A manifold is a topological space which locally looks like Cartesian n-space ℝn; it is built up of pieces of ℝn glued together by homeomorphisms. If these homeomorphisms are differentiable we obtain a differentiable manifold.
Il faut d’abord examiner la question de la définition des variétés.
P. Heegard, Dissertation, 1892
The assemblage of points on a surface is a twofold manifoldness ; the assemblage of points in tri-dimensional space is a threefold manifoldness; the values of a continuous function of n arguments an n-fold manifoldness.
G. Chrystal, Encyclopedia Brittanica, 1892
The introduction of numbers as coordinates ... is an act of violence ...
H. Weyl, Philosophy of Mathematics and Natural Science, 1949
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For r = 0 this is sometimes called a locally flat C0 submanifold.
This is in accordance with the principle that in mathematics a red herring does not have to be either red or a herring.
This means that D n(p) = {x∈ℝn:∣x∣ < p}; the unit disk is Δn = D n(1).
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© 1976 Springer-Verlag New York Inc.
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Hirsch, M.W. (1976). Manifolds and Maps. In: Differential Topology. Graduate Texts in Mathematics, vol 33. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9449-5_2
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DOI: https://doi.org/10.1007/978-1-4684-9449-5_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-9451-8
Online ISBN: 978-1-4684-9449-5
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