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A shape fibration is an adaptation of the notion of Hurewicz fibration from the setup of homotopy theory to shape theory (of locally compact metrisable spaces).
A map between metric compacta is called a shape fibration, provided it is induced by a level map of ANR-sequences satisfying the approximate homotopy lifting property with respect to any metric space and the lifting index, and lifting mesh do not depend on .
If, more generally, and are locally compact metric spaces. A proper map is a shape fibration if for any compact the restriction of to a map is a shape fibration between metric compacta.
If and are locally compact metric ANR’s then the notion of shape fibration coincides with a notion of an approximate fibration.
S. Mardešić, T. B. Rushing, Shape fibrations. I. General Topology Appl. 9 (1978), no. 3, 193–215.
S. Mardešić, J. Segal, (1982) Shape Theory, North Holland.
T. B. Rushing, Cell-like maps, approximate fibrations and shape fibrations
Last revised on May 17, 2017 at 11:56:18. See the history of this page for a list of all contributions to it.