identity map

Definition If X is a set, then the identity map in X is the mapping that maps each element in X to itself.

0.0.1 Properties

  1. 1.

    An identity map is always a bijection.

  2. 2.

    Suppose X has two topologiesMathworldPlanetmathPlanetmath τ1 and τ2. Then the identity mapping I:(X,τ1)(X,τ2) is continuous if and only if τ1 is finer than τ2, i.e., τ1τ2.

  3. 3.

    The identity map on the n-sphere, is homotopic ( to the antipodal map A:SnSn if n is odd [1].


Title identity map
Canonical name IdentityMap
Date of creation 2013-03-22 14:03:43
Last modified on 2013-03-22 14:03:43
Owner bwebste (988)
Last modified by bwebste (988)
Numerical id 7
Author bwebste (988)
Entry type Definition
Classification msc 03E20
Synonym identity mapping
Synonym identity operator
Synonym identity function
Related topic ZeroMap
Related topic IdentityMatrix