Članek je posvečen problemu F. D. Ancela o sovpadanju razredov finih homotopskih ekvivalenc in ekvivalenc med metričnimi prostori. Glavni rezultat se glasi: Bodi ▫$f: X\to Y$▫ preslikava med ...metričnima prostoroma in denimo, da za vsako pokritje ▫$\sigma \in {\rm cov}Y$▫ obstaja taka preslikava ▫$g: Y\to X$▫, da sta ▫${\rm id}_Y$▫ in ▫$f \circ g$▫ ▫$\sigma$▫-blizu, ▫${\rm id}_X$▫ in ▫$g \circ f$▫ sta ▫$f_{-1}(\sigma)$▫-homotopni in ▫$f \simeq f\circ g\circ f \; [{\rm rel}o]$▫. Potem je ▫$f$▫ fina homotopska ekvivalenca, če je ▫$X$▫ poln za neko metriko ▫$d$▫.
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