simply connected
A topological space
is said to be simply connected if it is path connected and the fundamental group
of the space is trivial (i.e. the one element group). What this means, basically, is that every path on the space can be shrunk to a point. This is equivalent
to saying that every path is contractible. A simply connected space can be visualized as a space with no “holes”.
Some basic examples of a simply connected space are the unit disc in , or the Riemann sphere. Non-examples of a simply connected space are the circle, the annulus, and a punctured plane (a plane with a point removed). In each of the non-examples, any closed curve around the “hole” is a path that can not be shrunk to a point.
| Title | simply connected |
|---|---|
| Canonical name | SimplyConnected |
| Date of creation | 2013-03-22 11:59:33 |
| Last modified on | 2013-03-22 11:59:33 |
| Owner | CWoo (3771) |
| Last modified by | CWoo (3771) |
| Numerical id | 9 |
| Author | CWoo (3771) |
| Entry type | Definition |
| Classification | msc 55P15 |
| Related topic | SemilocallySimplyConnected |