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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

Projective Plane Simplicial Complex Homology Group Closed Surface Open Disk 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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