Space in which every retraction is a deformation retraction
Definition
A space in which every retraction is a deformation retraction is a topological space with the property that any retraction for a subspace of (with the subspace topology) arises as a deformation retraction, i.e., there is a homotopy from the identity map to that retraction that restricts to on the subspace at all time.
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| nonempty topologically convex space | |FULL LIST, MORE INFO |
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| contractible space | |FULL LIST, MORE INFO | |||
| SDR-contractible space | |FULL LIST, MORE INFO |