State the definition of a covering space \[ p:\widetilde X\to X. \] Let \(f:Y\to X\) be a map having two lifts \[ \widetilde f_1,\widetilde f_2:Y\to\widetilde X. \] If \(Y\) is connected and the two lifts agree at one point of \(Y\), prove that \[ \widetilde f_1=\widetilde f_2 \] on all of \(Y\).
Uniqueness of lifts from a connected space
P-WESTOP08-II4
- Area
- Topology
- Seen at
- WESLEYAN
- Years
- 2008
- Status
- draft