Homotopy

Definition

Suppose $X,Y$ are topological spaces and $f,g:X\to Y$ are continuous maps from $X$ to $Y$. A continuous map $F:X\times I\to Y$ is termed a homotopy from $f$ to $g$ if for every $x\in X$, $F(x,0)=f(x)$ and $F(x,1)=g(x)$.

Related notions

• Self-homotopy. Also check out Category:Properties of self-homotopies
• Smooth homotopy and piecewise smooth homotopy
• Linear homotopy and piecewise linear homotopy

Facts

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