$x \mapsto x^3$, from $\reals$ to $\reals$

Example · Undergraduate

Terms

Term	This example	Why
continuous	✓	$x \mapsto x^3$ is a homeomorphism of $\reals$: it is continuous, with the continuous inverse $x \mapsto \sqrt[3]{x}$. So it maps open sets to open sets and closed sets to closed sets.
open map	✓
closed map	✓

All examples · All distinctions · All definitions