homeomorphisms preserve connected components
Proof. Take any . Because is continuous is connected, then there exists such that (because is a connected component). Now is a homeomorphism, , is connected and is a connected component, so . Thus , which completes the proof.
|Title||homeomorphisms preserve connected components|
|Date of creation||2013-03-22 18:45:32|
|Last modified on||2013-03-22 18:45:32|
|Last modified by||joking (16130)|