Pronunciations (6)
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/ˈkləʊ̯.pən/
Pronunciation notes
- Received-Pronunciation
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/ˈkloʊ̯.pən/
Pronunciation notes
- Canada
- General-American
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/ˈklɐʉ̯.pən/
Pronunciation notes
- Australia
- New-Zealand
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/ˈkləʉ̯.pən/
Pronunciation notes
- Australia
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/ˈklo.pən/
Pronunciation notes
- Scotland
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/ˈkloː.pen/
Pronunciation notes
- India
Adjective
Both open and closed.
Usage- not-comparable
- of a set in a topological space
- Related words
- the half-open interval defined there is not to be confused with the clopen set
- Examples
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More examples (1)
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.
FACT 1. Disjoint closed subsets of #92;mathbb#123;N#125;#92;mathbb#123;N#125; may be separated by disjoint clopen sets.
More examples (1)
Theorem 3. 1) Every two disjoint closed sets in a totally disconnected compact space #92;mathfrak#123;Q#125; 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.
Noun
A pair of work shifts in which a worker works a closing shift one day and then works an opening shift the following day.
- Related words
- Examples
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James is on vacation, so I've got to do a clopen this weekend to cover his shifts.