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.
Source: wiktionary
Clopen
//ˈkləʊ̯.pən//
Synonyms for "clopen"
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FACT 1. Disjoint closed subsets of #92;mathbb#123;N#125;#92;mathbb#123;N#125; may be separated by disjoint clopen sets.
Source: wiktionary
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.
Source: wiktionary
James is on vacation, so I've got to do a clopen this weekend to cover his shifts.
Source: wiktionary
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Data sourced from Wiktionary, WordNet, CMU, and other open linguistic databases. Updated March 2026.