pointed topological space
Definition Suppose X is a non-empty topological space
and x0 is an
element of X. Then the pair (X,x0) 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 |