Weak retract

This article defines a property over pairs of a topological space and a subspace, or equivalently, properties over subspace embeddings (viz, subsets) in topological spaces

Definition

A subspace of a topological space is said to be a weak retract if there is a weak retraction from the whole space to the subspace. A weak retraction here is a continuous map from a space to itself such that the restriction of the map to its image, is a homeomorphism from the image to itself (for a retraction, we require the homeomorphism to be the identity map).

Relation with other properties

Stronger properties

• Retract

Weaker properties

• Homologically injective subspace
• Homotopically injective subspace