clopen

English

English Wikipedia has an article on:

clopen set

Wikipedia

Etymology

Blend of closed +‎ open.

Pronunciation

• enPR: klō′pən
• (Received Pronunciation) IPA^(key): /ˈkləʊ̯.pən/
• (General American, Canada) IPA^(key): /ˈkloʊ̯.pən/
• (General Australian, New Zealand) IPA^(key): /ˈklɐʉ̯.pən/

  (General Australian) IPA^(key): /ˈkləʉ̯.pən/

• (Scotland) IPA^(key): /ˈklo.pən/
• (India) IPA^(key): /ˈkloː.pen/
• Rhymes: -əʊpən
• Hyphenation: clo‧pen

Adjective

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, 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”, in Krzysztof Jarosz, editor, Function Spaces: Proceedings of the Third Conference on Function Spaces (Contemporary Mathematics), volume 232, American Mathematical Society, page 124:

     FACT 1. Disjoint closed subsets of ${\displaystyle \mathbb {N} ^{\mathbb {N} }}$ may be separated by disjoint clopen sets.

   • 2002, D. A. Vladimirov, Boolean Algebras in Analysis‎, page 133:

     Theorem 3. 1) Every two disjoint closed sets in a totally disconnected compact space ${\displaystyle {\mathfrak {Q}}}$ 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.

See also

• Interval (mathematics) § Definitions and terminology on WikipediaWikipedia ; the half-open interval defined there is not to be confused with the clopen set.

Noun

clopen (plural clopens)

1. A pair of work shifts in which a worker works a closing shift one day and then works an opening shift the following day.

   James is on vacation, so I've got to do a clopen this weekend to cover his shifts.

See also

• swing shift

Further reading

• “clopen”, in OneLook Dictionary Search.

Anagrams

• Coplen