Category:Definitions/Paths (Topology)

This category contains definitions related to paths in the context of topology.
Related results can be found in Category:Paths (Topology).

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

Let $I \subset \R$ be the closed real interval $\closedint a b$.

A path in $T$ is a continuous mapping $\gamma: I \to S$.

The mapping $\gamma$ can be referred as:

a path (in $T$) joining $\map \gamma a$ and $\map \gamma b$

or:

a path (in $T$) from $\map \gamma a$ to $\map \gamma b$.