A topological subspace is a neighborhood retract of a topological space if there is a neighborhood in such that is a retract of .
A metrisable topological space is an absolute neighborhood retract if for any embedding as a closed subspace in a metrisable topological space , is a neighborhood retract of .
A pair where is a closed subspace of is an NDR-pair or a closed Borsuk pair if there is a function and a homotopy such that , for all , for all , for all such that and . (See deformation retract.)
The canonical inclusion corresponding to any NDR-pair is a Hurewicz cofibration.
Revised on April 3, 2012 17:22:21
by Urs Schreiber