We prove that a metric space is an ANR if, and only if, every open subset of X has the homotopy type of a CW-complex.
@article{bwmeta1.element.bwnjournal-article-fmv144i1p11bwm, author = {Robert Cauty}, title = {Une caract\'erisation des r\'etractes absolus de voisinage}, journal = {Fundamenta Mathematicae}, volume = {144}, year = {1994}, pages = {11-22}, language = {fr}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv144i1p11bwm} }
Cauty, Robert. Une caractérisation des rétractes absolus de voisinage. Fundamenta Mathematicae, Tome 144 (1994) pp. 11-22. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv144i1p11bwm/
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