The approximate homotopy lifting property is a weak version of the homotopy lifting property in the setup of metric spaces.
A proper map between locally compact metric absolute neighborhood retracts (ANRs) satisfies the approximate homotopy lifting property for a space if for any open covering of B, and any map with a homotopy such that , there exists a homotopy such that and the maps and are -close?.
A proper map between locally compact metric ANRs is an approximate fibration if has the approximate homotopy lifting property for all metric spaces.
It is straightfoward to generalize this notion to the level maps of inverse systems of locally compact metric ANRs.
Last revised on December 24, 2009 at 02:25:27. See the history of this page for a list of all contributions to it.