chapter  7
5 Pages

Loop Spaces and Higher Homotopy Groups

WithMarvin J. Greenberg, John R. Harper

Let XI be the set of all paths in X. If X is a metric space with metric d, we can define a metric d * on XI by d ∗ ( σ , τ ) = sup t ∈ I     d ( σ ( t ) , τ ( t ) )