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added 110 characters in body

edited Sep 17, 2016 at 20:33

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There is a theorem of Dold to this effect:

Dold, Albrecht Die Homotopieerweiterungseigenschaft (=HEP) ist eine lokale Eigenschaft. (German) Invent. Math. 6 1968 185–189.

answered Sep 17, 2016 at 20:23

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