# Category:Definitions/Arc-Connected Spaces

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This category contains definitions related to Arc-Connected Spaces.

Related results can be found in **Category:Arc-Connected Spaces**.

Let $T = \struct {S, \tau}$ be a topological space.

Then $T$ is **arc-connected** if and only if every two points in $T$ are arc-connected in $T$.

That is, $T$ is **arc-connected** if and only if:

- $\forall x, y \in S: \exists$ a continuous injection $f: \closedint 0 1 \to X$ such that $\map f 0 = x$ and $\map f 1 = y$.

## Pages in category "Definitions/Arc-Connected Spaces"

The following 14 pages are in this category, out of 14 total.

### A

- Definition:Arc (Topology)
- Definition:Arc Component
- Definition:Arc Connected
- Definition:Arc-Connected
- Definition:Arc-Connected Points
- Definition:Arc-Connected Set
- Definition:Arc-Connected Space
- Definition:Arc-Connected/Also known as
- Definition:Arc-Connected/Points
- Definition:Arc-Connected/Subset
- Definition:Arc-Connected/Topological Space
- Definition:Arc-Wise Connected
- Definition:Arcwise Connected
- Definition:Arcwise-Connected