Local homeomorphism
= Local homeomorphism
{wiki}
= Homeomorphic
{synonym}
A local homeomorphism is a continuous map $f:X\to Y$ such that every point of $X$ has a neighbourhood on which $f$ restricts to a homeomorphism onto an open subset of $Y$.
A homeomorphism is a bijective continuous map whose inverse is continuous. Two spaces related by one have the same topological properties.