pointed topological space

Definition Suppose X is a non-empty topological spaceMathworldPlanetmath and x0 is an element of X. Then the pair (X,x0) is called a pointed topological spacePlanetmathPlanetmath, or a based topological space.

The idea with pointed topological spaces is simply that one fixes a base point in the space. This is necessary, for instance, when defining the fundamental groupMathworldPlanetmathPlanetmath of a topological space.

Title pointed topological space
Canonical name PointedTopologicalSpace
Date of creation 2013-03-22 14:01:15
Last modified on 2013-03-22 14:01:15
Owner bwebste (988)
Last modified by bwebste (988)
Numerical id 7
Author bwebste (988)
Entry type Definition
Classification msc 54-00
Classification msc 54E99
Synonym based topological space
Related topic CategoryOfPointedTopologicalSpaces
Related topic PolishGSpace
Related topic OmegaSpectrum