Étale map

Definition
Let $$X$$ and $$Y$$ be topological spaces. A continuous map $$f:X \to Y$$ is termed an étale map if it is surjective, is a local homeomorphism, and if every fiber $$f^{-1}(y)$$ is discrete with the subspace topology.

Stronger properties

 * Covering map

Weaker properties

 * Local homeomorphism
 * Open map
 * Quotient map

Incomparable properties

 * Bundle map (the map associated to a fiber bundle): A map which is both an etale map and a bundle map is a covering map