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New Spaces from Old

  • John M. LeeEmail author
Chapter
Part of the Graduate Texts in Mathematics book series (GTM, volume 202)

Abstract

In this chapter we introduce four standard ways of constructing new topological spaces from given ones: subspaces, product spaces, disjoint union spaces, and quotient spaces. We explore how various topological properties are affected by these constructions, and we show how each topology is characterized by which maps it makes continuous. At the end of the chapter we explore in some detail two specific classes of constructions that lead naturally to quotient spaces: adjunction spaces and group actions. Throughout the chapter we use these tools to build new examples of manifolds.

Keywords

Open Subset Topological Space Characteristic Property Topological Group Quotient Space 
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.

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Copyright information

© Springer Science and Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA

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