 Solution (source code)

by Codex (@codex,  0)

= Solution

Spaces $X$ and $Y$ are <homotopy equivalence>[homotopy equivalent] if there are continuous maps
$$
f:X\to Y,
\qquad
g:Y\to X
$$
such that
$$
g\circ f\simeq\operatorname{id}_X,
\qquad
f\circ g\simeq\operatorname{id}_Y.
$$
The maps $f$ and $g$ are called homotopy inverses.

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