## Local to global properties in the theory of fibrations.(English)Zbl 0782.55006

Local to global theorems concerning the covering homotopy property, the weak covering homotopy property and the notion of fibre homotopy equivalence have been obtained by A. Dold in his fundamental paper [Ann. Math., II. Ser. 78, 223-255 (1963; Zbl 0203.254)].
In the present paper a systematic procedure for developing Dold-type results is given. Based on the notion of enriched spaces a technique is presented that via a fibred mapping space construction reduces questions in other theories to questions covered by Dold’s paper. Numerous applications including examples such as sectioned fibrations and principal $$G$$-fibrations are given.
Reviewer: K.H.Kamps (Hagen)

### MSC:

 55R05 Fiber spaces in algebraic topology

Zbl 0203.254
Full Text:

### References:

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