Definition:Straight-Line Homotopy
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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 $g$).
Sources
- 2011: John M. Lee: Introduction to Topological Manifolds (2nd ed.) ... (previous) ... (next): $\S 7$: Homotopy and the Fundamental Group. Homotopy