# Category:Components

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This category contains results about **Components** in the context of **Topology**.

From Connectedness of Points is Equivalence Relation, $\sim$ is an equivalence relation.

From the Fundamental Theorem on Equivalence Relations, the points in $T$ can be partitioned into equivalence classes.

These equivalence classes are called the **(connected) components** of $T$.

If $x \in S$, then the **component of $T$ containing $x$** (that is, the set of points $y \in S$ with $x \sim y$) is denoted by $\map {\operatorname {Comp}_x} T$.

## Pages in category "Components"

The following 11 pages are in this category, out of 11 total.

### C

- Complement of Bounded Set in Complex Plane has at most One Unbounded Component
- Component is not necessarily Path Component
- Component of Locally Connected Space is Open
- Components are Open iff Union of Open Connected Sets
- Components are Open iff Union of Open Connected Sets/Components are Open implies Space is Union of Open Connected Sets
- Components are Open iff Union of Open Connected Sets/Lemma 1
- Components are Open iff Union of Open Connected Sets/Space is Union of Open Connected Sets implies Components are Open
- Connected Component is Closed