View source for Clopen

==English==
{{wikipedia|Clopen set}}

===Etymology===
{{blend|en|closed|open}}.

===Pronunciation===
* {{IPA|en|/ˈkləʊ.pən/|a=RP}}
* {{IPA|en|/ˈkloʊ.pən/|a=US}}
* {{rhymes|en|əʊpən|s=2}}

===Adjective===
{{en-adj|-}}

# {{lb|en|topology|of a [[set]] in a [[topological space]]}} Both [[open]] and [[closed]].
#* {{quote-text|en|year=1990|author=Gerald A Edgar|title=Measure, Topology, and Fractal Geometry|page=80|url=https://books.google.com.au/books?id=UJ3lBwAAQBAJ&pg=PA80&dq=%22clopen%22&hl=en&sa=X&ved=0ahUKEwijuaGs5YbOAhVDHGMKHazHCd0Q6AEIHTAA#v=onepage&q=%22clopen%22&f=false|passage=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'', {{w|American Mathematical Society}}, Contemporary Mathematics, Volume 232, [https://books.google.com.au/books?id=CT0bCAAAQBAJ&pg=PA124&dq=%22clopen%22&hl=en&sa=X&ved=0ahUKEwijuaGs5YbOAhVDHGMKHazHCd0Q6AEIgAEwEA#v=onepage&q=%22clopen%22&f=false page 124],
#*: FACT 1. Disjoint closed subsets of <math>\mathbb{N}^\mathbb{N}</math> may be separated by disjoint '''clopen''' sets.
#* {{quote-text|en|year=2002|author=D. A. Vladimirov|title=Boolean Algebras in Analysis|page=133|url=https://books.google.com.au/books?id=Y9ryCAAAQBAJ&pg=PA133&dq=%22clopen%22&hl=en&sa=X&ved=0ahUKEwijuaGs5YbOAhVDHGMKHazHCd0Q6AEIIzAB#v=onepage&q=%22clopen%22&f=false|passage='''Theorem 3.''' 1) ''Every two disjoint closed sets in a totally disconnected compact space <math>\mathfrak{Q}</math> are separated by disjoint '''clopen''' sets.''<br>2) ''Every algebra of '''clopen''' sets which separates the points of a totally disconnected compact space contains all '''clopen''' sets.''}}

===Noun===
{{en-noun}}

# A pair of [[work]] [[shift]]s in which a [[worker]] works a [[closing shift]] one day and then works an [[opening shift]] the following day.
#: {{usex|en|James is on vacation, so I've got to do a '''clopen''' this weekend to cover his shifts.}}

====See also====
* {{l|en|swing shift}}

===Anagrams===
* {{anagrams|en|a=celnop|Coplen}}

{{cln|en|adjectives ending in -en}}