Adjunction spaces are an example of pushouts in Top.

Adjunction spaces are also used to define connected sums of manifolds.

That is to say, the adjunction space is universal with respect to following commutative diagram:

Discusses their homotopy type, and uses adjunction spaces as an introduction to (finite) cell complexes.

Adjunction space.

The construction of adjunction spaces is an example of pushouts in the category of topological spaces.

In mathematics, an adjunction space (or attaching space) is a common construction in topology where one topological space is attached or "glued" onto another.

In the category of abelian groups, pushouts can be thought of as "direct sum with gluing" in the same way we think of adjunction spaces as "disjoint union with gluing".