clopen

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English[edit]

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Etymology[edit]

Blend of closed +‎ open.

Pronunciation[edit]

Adjective[edit]

clopen (not comparable)

  1. (topology, of a set in a topological space) Both open and closed.
    • 1990, Gerald A Edgar, Measure, Topology, and Fractal Geometry[1], page 80:
      A subset of a metric space is clopen iff it is both closed and open. A metric space is called zero-dimensional iff there is a base for the open sets consisting of clopen sets.
    • 1999, S. J. Dilworth, On the extensibility of certain homeomorphisms and linear isometries, Krzysztof Jarosz (editor), Function Spaces: Proceedings of the Third Conference on Function Spaces, American Mathematical Society, Contemporary Mathematics, Volume 232, page 124,
      FACT 1. Disjoint closed subsets of may be separated by disjoint clopen sets.
    • 2002, D. A. Vladimirov, Boolean Algebras in Analysis[2], page 133:
      Theorem 3. 1) Every two disjoint closed sets in a totally disconnected compact space are separated by disjoint clopen sets.
      2) Every algebra of clopen sets which separates the points of a totally disconnected compact space contains all clopen sets.

Anagrams[edit]