absolute retract
absolute retract
[¦ab·sə‚lüt ri′trakt] (mathematics)
A topological space, A, such that, if B is a closed subset of another topological space, C, and if A is homeomorphic to B, then B is a retract of C.
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Note that any absolute retract (AR-space) is an AMR-space and any absolute neighbourhood retract (ANR-space) is an ANMR-space.
A space X is called an [R.sub.[delta]]-set if there exists a decreasing sequence {[X.sub.n]} of compact absolute retracts such that X = [[intersection].sub.n] [X.sub.n].
sets which are homologically equivalent to one point spaces) contains, besides standard convex sets, more general absolute retracts, R-sets and contractible sets (i.e.
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