# clopen

## English

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### Etymology

Blend of closed +‎ open.

### Pronunciation

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 ${\displaystyle \mathbb {N} ^{\mathbb {N} }}$ 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 ${\displaystyle {\mathfrak {Q}}}$ 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.

### 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.