Definition:Straight-Line Homotopy

Definition
Let $X$ and $Y$ be topological spaces.

Let $f: X \to Y$, $g: X \to Y$ be continuous mappings.

Let $H: X \times \closedint 0 1 \to Y$ be the homotopy between $f$ and $g$ such that:


 * $\forall x \in X : \forall t \in \closedint 0 1 : \map H {x, t} = \map f x + t \paren {\map g x - \map f x}$

Then $H$ is called the straight-line homotopy (between $f$ and $g$).