Assertion: isomorphism | /r/Synonym | diffeomorphism
Facets:
value: in mathematical analysis
type: OTHER
Source sentences:
text: In mathematical analysis, when the morphisms are differentiable functions, isomorphisms are also called diffeomorphisms.
text: Isomorphisms in $\mathsf{Set}$ are called bijections, isomorphisms in $\mathsf{Top}$ are called homeomorphisms, isomorphisms in $\mathsf{Man}$ (the category of smooth manifolds and smooth maps) are called diffeomorphisms, isomorphisms in $\mathsf{Vect}_{\mathbb{k}}$ (the category of $\mathbb{k}$-vector spaces with linear transformations) are called, well, isomorphisms, and so on.
text: In mathematical analysis, where the morphisms are differentiable functions, isomorphisms are also called diffeomorphisms.