Étale map

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This article defines a property of continuous maps between topological spaces


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.

Relation with other properties

Stronger properties

Weaker properties

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