Category:Arc-Connected Spaces
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This category contains results about Arc-Connected Spaces.
Definitions specific to this category can be found in Definitions/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 $\map f 1 = y$.
Subcategories
This category has the following 3 subcategories, out of 3 total.
A
- Arc Components (2 P)
- Arcs (Topology) (empty)
L
- Locally Arc-Connected Spaces (8 P)
Pages in category "Arc-Connected Spaces"
The following 14 pages are in this category, out of 14 total.