General Topology/Homotopy

This means that $$H$$ is a "continuous transformation" of $$f$$ into $$g$$ or vice versa.

Note that the first argument is denoted in the lower index, so that instead of $$r(t,x)$$ we write $$r_t(x)$$.

That is, a deformation retraction is a homotopy between the identity and a retract onto $$A$$.