# clopen

## English

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### Etymology

Blend of closed +‎ open.

### Pronunciation

FACT 1. Disjoint closed subsets of ${\displaystyle \mathbb {N} ^{\mathbb {N} }}$ may be separated by disjoint clopen sets.
Theorem 3. 1) Every two disjoint closed sets in a totally disconnected compact space ${\displaystyle {\mathfrak {Q}}}$ are separated by disjoint clopen sets.