Proof That Continuous Functions From a Topological Space To The Real Numbers With The Euclidean Topology Are Homotopic
Theorem
Ifandare continuous, thenandare homotopic.
Proof
Letandbe continuous functions.andare said to be homotopic if can be 'morphed' ontoand vice versa, or more concisely, if a continuous functionexists such thatand
Ifdefinethenandare homotopic.