Fundamental Concepts

  • Davide L. FerrarioEmail author
  • Renzo A. Piccinini
Part of the CMS Books in Mathematics book series (CMSBM)


Let X be a given set. A topology on X is a set \(\mathfrak{U}\) of subsets of X satisfying the following properties: A1 \(\varnothing, X \in \mathfrak{U}\); A2 if {U α | α ∈ J} is a set of elements of \(\mathfrak{U}\), then
$${\bigcup \nolimits }_{\alpha \in J}{U}_{\alpha } \in \mathfrak{U};$$
A3 if \(\{{U}_{\alpha }\vert \alpha = 1,\ldots, n\}\) is a finite set of elements of \(\mathfrak{U}\), then
$${\bigcap \nolimits }_{\alpha =1}^{n}{U}_{ \alpha } \in \mathfrak{U}.$$


Abelian Group Topological Space Topological Group Compact Space Homotopy Class 
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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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