# Category:Path-Connected Spaces

This category contains results about Path-Connected Spaces.
Definitions specific to this category can be found in Definitions/Path-Connected Spaces.

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

Then $T$ is a path-connected space if and only if $S$ is a path-connected set of $T$.

That is, $T$ is a path-connected space if and only if:

for every $x, y \in S$, there exists a continuous mapping $f: \closedint 0 1 \to S$ such that $\map f 0 = x$ and $\map f 1 = y$.

## Subcategories

This category has the following 6 subcategories, out of 6 total.

## Pages in category "Path-Connected Spaces"

The following 32 pages are in this category, out of 32 total.