clopen
Collocations
3ADJ.
disjoint, metric
VERB + CLOPEN
consisting, separated, sets
CLOPEN + NOUN
iff, weekend
Definitions
adj
Both open and closed.
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.
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.
James is on vacation, so I've got to do a clopen this weekend to cover his shifts.
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Idioms & Phrases
Example Bank
4A 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.
WiktionaryFACT 1. Disjoint closed subsets of #92;mathbb#123;N#125;#92;mathbb#123;N#125; may be separated by disjoint clopen sets.
WiktionaryTheorem 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
WiktionaryJames is on vacation, so I've got to do a clopen this weekend to cover his shifts.
Wiktionary