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What does compactify mean?

Looking for the meaning or definition of the word compactify? Here's what it means.

Verb
  1. (humorous) To become compact or more compact.
  2. (humorous) To render (a thing) compact or more compact.
  3. (mathematics) To enlarge (a topological space) in order to render it compact.
  4. (physics) To adjust a theory so as to render finite or periodic (a theoretical space-time dimension).
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Examples
Artificially compactify the choice set in the following way.

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