Theorem
Ifand
are continuous functions and
is homotopic to
- written
then
is homotopic to
Proof
Sincethere is a homotopy
with
Defineby
Thenand
Sinceis continuous, so is
and
Theorem
Ifand
are continuous functions and
is homotopic to
- written
then
is homotopic to
Proof
Sincethere is a homotopy
with
Defineby
Thenand
Sinceis continuous, so is
and