pointed topological space

Definition Suppose $X$ is a non-empty topological space and $x_0$ is an element of $X$. Then the pair $(X,x_0)$ is called a pointed topological space, 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 group 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