compactification

Noun

Meaning

(topology) Any of various procedures of enlarging a topological space to make it compact.

(topology) The space resulting from any such procedure.

(physics) Any modification of a theory such that an infinite parameter becomes finite.

(physics) The reduction of the number of large spacetime dimensions of a physical theory by making some of them compact.

Phrases with the word

Examples

Also, a subset of a normal space need not be normal (i.e. not every normal Hausdorff space is a completely normal Hausdorff space), since every Tychonoff space is a subset of its Stone–Čech compactification (which is normal Hausdorff). Source: Internet

Becker, Becker, and Schwarz 2007, p. 12 Number of dimensions main An example of compactification : At large distances, a two dimensional surface with one circular dimension looks one-dimensional. Source: Internet

But in fact, there is a simpler method available in the locally compact case; the one-point compactification will embed X in a compact Hausdorff space a(X) with just one extra point. Source: Internet

Every sequence that ran off to infinity in the real line will then converge to ∞ in this compactification. Source: Internet

Forming the one-point compactification a(X) of X corresponds under this duality to adjoining an identity element to C 0 (X). Source: Internet

For such spaces the Alexandroff extension is called the one-point compactification or Alexandroff compactification. Source: Internet

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