Index

This illustrates the process of lifting a homotopy $h\colon [0,1]^2\to Y$
over a covering map $p\colon X\to Y$. We divide $[0,1]^2$ into
small rectangles $Q$ such that $h(Q)$ is contained in an open set
that is trivially covered by $p$. We then work through all these
rectangles in a series of stripes, lifting $h$ over each
rectangle in turn. For each rectangle $Q$, there are an infinite
number of possible lifts of $h|_Q$. At the first stage, we can
choose any one of those lifts. At every subsequenct stage, there
is only one possible lift that matches up with what we have
already done.