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A characterization of absolute neighborhood retracts. (Une caractérisation des rétractes absolus de voisinage.) (French) Zbl 0812.54026

Solving a problem of R. Geoghegan it is proved that a metrix space \(X\) is an ANR iff every open subset of \(X\) has the homotopy type of a CW- complex.

MSC:

54C55 Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties)
55M15 Absolute neighborhood retracts
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