Space in which every retraction is a deformation retraction

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Definition

A space in which every retraction is a deformation retraction is a topological space X with the property that any retraction math>r:X \to Y</math> for a subspace Y of X (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 r on the subspace Y at all time.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
topologically convex space Template:Intermediate notions

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