What does clopen mean?
Clopen means (topology, of a set in a topological space) Both open and closed..
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/ˈkləʊ̯.pən/ · adjective
(topology, of a set in a topological space) 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.
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.
James is on vacation, so I've got to do a clopen this weekend to cover his shifts.
Use clopen when its meaning, tone and grammar fit the full sentence. A synonym is not always a direct replacement.
Clopen means (topology, of a set in a topological space) Both open and closed..
The closest synonym depends on the sentence and intended sense.
The opposite depends on the specific sense.
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.
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