# Arc

A topological space $(X,\tau)$ is called an *arc* if it is homeomorphic to the real interval $[0,1]$. If $h \colon [0,1] \rightarrow X$ is a homeomorphism onto the arc $X$ then the *end points of the arc $X$* are the points $h(0)$ and $h(1)$.

## Properties of arcs

**Theorem:** If $X$ is an arc then $X$ is a continuum.