Étale map: Difference between revisions
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{{continuous map property}} | {{continuous map property}} | ||
==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 '''etale 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== | |||
===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]] | |||
Revision as of 19:29, 2 December 2007
This article defines a property of continuous maps between topological spaces
Definition
Let and be topological spaces. A continuous map is termed an etale 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