# closed

## EnglishEdit

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### PronunciationEdit

closed (not comparable)

1. Sealed, made inaccessible or impassable; not open.
3. Not public.
closed source
a closed committee
4. (topology, of a set) Having an open complement.
5. (mathematics, of a set) Such that its image under the specified operation is contained in it.
The set of integers is closed under addition: ${\displaystyle \forall x,y\in \mathbb {Z} \,x+y\in \mathbb {Z} }$ .
6. (mathematics, logic, of a formula) Lacking a free variable.
7. (graph theory, of a walk) Whose first and last vertices are the same, forming a closed loop.

#### TranslationsEdit

The translations below need to be checked and inserted above into the appropriate translation tables, removing any numbers. Numbers do not necessarily match those in definitions. See instructions at Wiktionary:Entry layout#Translations.

### VerbEdit

closed

1. simple past tense and past participle of close

## WelshEdit

### NounEdit

closed m (plural closedau)

1. Alternative form of closet

Welsh mutation