closed set

Set whose complement is an open set

Entitytype of setQ320357

Also known as closed subset

Instance of: type of set
Subclass of: Fσ set
Part of: list of types of sets

Overview

From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0

In topology, a branch of mathematics, a closed set is a set that contains all of its boundary points. An example is the closed interval , which is closed in the real line because it includes both points and of its boundary. A point is on the boundary if every neighbourhood of it meets both the set and its complement. A set is thus closed if it is equal to its closure, the set obtained by adjoining all boundary points to it.

Overview

All data

21 statements · 10% with external sources · numbers in brackets are citations

Opposite of: open set
Members / parts: boundary
interior
Studied by: topology

On other databases

14 identifiers linking closed set across the web's reference databases

Data quality

statements

10%

externally sourced

Source last edited September 6, 2026. AIDB refreshes this page daily.

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AIDB. (2026). closed set (Q320357). Retrieved from https://aidb.si/e/closed-set-Q320357