New Spaces from Old
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.
KeywordsOpen Subset Topological Space Characteristic Property Topological Group Quotient Space
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