Proof That Continuous Functions From a Topological Space To The Real Numbers With The Euclidean Topology Are Homotopic
Theorem
If
and
are continuous, then
and
are homotopic.
Proof
Let
and
be continuous functions.andare said to be homotopic if can be 'morphed' ontoand vice versa, or more concisely, if a continuous function
exists such that
and
If
define
thenandare homotopic.
