 Homotopy

A homotopy between maps $f,g:Y\to X$ is a continuous map $H:Y\times [0,1]\to X$ with $H(y,0)=f(y)$ and $H(y,1)=g(y)$.

Homotopy is a concept in topology, a branch of mathematics that studies the properties and structures of spaces that are preserved under continuous transformations. More specifically, homotopy provides a way to classify continuous functions between topological spaces based on their ability to be deformed into one another.