Vol. 65, No. 2, 1976

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An approximation theorem for maps into Kan fibrations

Rudolf Fritsch

Vol. 65 (1976), No. 2, 347–351

In this note we prove that a semisimplicial map into the base of a Kan fibration having a continuous lifting to the total space also has a semisimplicial lifiting, very “close” to a given continuous lifting. As a special case we obtain a new proof of the famous Milnor-Lamotke theorem that a Kan set is a strong deformation retract of the singular set of its geometric realization.

Mathematical Subject Classification
Primary: 55J10, 55J10
Received: 8 October 1975
Revised: 3 March 1976
Published: 1 August 1976
Rudolf Fritsch