Chapter: Construction of Topologies

Sometimes, there is a need to construct a topology for a given set $X$ that suits some purpose by fulfilling certain properties. In this chapter, we discuss different ways that allow us to construct topologies.

  1. Definition: Topological Subspaces and Subspace Topologies
  2. Definition: Hereditary and Weakly Hereditary Properties
  3. Proposition: Construction of Topological Spaces Using a Subbasis
  4. Definition: Topological Sum, Disjoint Union
  5. Definition: Topological Product, Product Topology
  6. Definition: Subbasis and Basis of Topology

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  2. Jänich, Klaus: "Topologie", Springer, 2001, 7th Edition
  3. Grotemeyer, K.P.: "Topologie", B.I.-Wissenschaftsverlag, 1969