Meaning of clopen | Babel Free

Definitions

Both open and closed.

not-comparable

Examples

“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.”

CEFR level