Part: Metric Spaces

The so-called metric spaces play in the topology a prominent role. An underlying concept of these spaces is the concept of a distance or metric. It is more intuitive than concepts set-theoretic topology, however, it is not as general and therefore, not always applicable. A typical example of a metric space is the multidimensional space of real numbers $\mathbb R^n.$ Even more specialized metric spaces are normed metric spaces especially suitable to describe vector spaces.

  1. Definition: Metric (Distance)
  2. Definition: Metric Space
  3. Definition: Open Sets in Metric Spaces
  4. Definition: Open Ball, Neighborhood
  5. Definition: Diameter In Metric Spaces
  6. Proposition: Metric Spaces and Empty Sets are Clopen

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