Compactification (mathematics) - Other Compactification Theories

Other Compactification Theories

  • The theories of ends of a space and prime ends.
  • Some 'boundary' theories such as the collaring of an open manifold, Martin boundary, Shilov boundary and Fürstenberg boundary.
  • The Bohr compactification of a topological group arises from the consideration of almost periodic functions.
  • One can compactify a topological ring by forming a projective line with inversive ring geometry.
  • The Baily-Borel compactification of a quotient of a hermitean symmetric space.
  • The wonderful compactification of a quotient of algebraic groups.

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    Our books of science, as they improve in accuracy, are in danger of losing the freshness and vigor and readiness to appreciate the real laws of Nature, which is a marked merit in the ofttimes false theories of the ancients.
    Henry David Thoreau (1817–1862)