# 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 PointedTopologicalSpace 2013-03-22 14:01:15 2013-03-22 14:01:15 bwebste (988) bwebste (988) 7 bwebste (988) Definition msc 54-00 msc 54E99 based topological space CategoryOfPointedTopologicalSpaces PolishGSpace OmegaSpectrum