A closed immersion is stable under base change and composition.

Note however that this set of rotations is not closed under composition.

The set of all Möbius transformations forms a group under composition.

Owing to the above properties, the set of all rotations is a group under composition.

This will not be the case with a general rotation in 3-space, which do form a closed set under composition.

The album was recorded under new composition of the band:

A smooth morphism is stable under base change and composition.

It can be seen fairly easily that this space forms a group under functional composition.

Maps in an allegory are closed under identity and composition.

Hence the set of quasiconformal maps forms a group under composition.