Étale map: Difference between revisions
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==Definition== | ==Definition== | ||
Let <math>X</math> and <math>Y</math> be [[topological space]]s. A [[continuous map]] <math>f:X \to Y</math> is termed an ''' | Let <math>X</math> and <math>Y</math> be [[topological space]]s. A [[continuous map]] <math>f:X \to Y</math> is termed an '''étale map''' if it is surjective, is a [[local homeomorphism]], and if every fiber <math>f^{-1}(y)</math> is discrete with the subspace topology. | ||
==Relation with other properties== | ==Relation with other properties== | ||
Latest revision as of 20:00, 11 May 2008
This article defines a property of continuous maps between topological spaces
Definition
Let and be topological spaces. A continuous map is termed an étale map if it is surjective, is a local homeomorphism, and if every fiber 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