Chapter: Density and Countability

The discoveries of Georg Cantor (1845 - 1918) regarding cardinal numbers and the comparison of the cardinalities of the infinite sets of the natural numbers":bookofproofs$718 $\mathbb N$, the "rational numbers":[bookofproofs$1033] $\mathbb Q,$ and the real numbers $\mathbb R$ motivate defining the concepts related to density in more general, topological terms, which we will do in this chapter.

  1. Definition: Dense Sets, Nowhere Dense Sets
  2. Definition: First and Second Category Sets

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  2. Jänich, Klaus: "Topologie", Springer, 2001, 7th Edition