Triangulable Manifolds

Chapter
Part of the CMS Books in Mathematics book series (CMSBM)

Abstract

A Hausdorff topological space X is called an n-dimensional manifold or simply an n-manifold, if for every point xX there exists an open set U of X that contains x and is homeomorphic to an open set of n . Hence, an n-manifold X is characterized by a set \(\mathfrak{A} =\{ ({U}_{i},{\phi }_{i})\ \vert \ i \in J\}\), where U i are open sets covering X, and ϕ i is a homeomorphism from U i onto an open set of n . The set \(\mathfrak{A}\) is the atlas of X and each pair (U i , ϕ i ) is a chart of X.

Keywords

Manifold 

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Dipartimento di Matematica e ApplicazioniUniversità di Milano-BicoccaMilanoItaly
  2. 2.Department of Mathematics and StatisticsDalhousie UniversityHalifaxCanada

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