Page "Manifold" Paragraph 30

Why does one study manifolds?

Manifolds, and generalized spaces composed of manifolds such as stratified spaces, occupy a central role in topology.

This is for a variety of reasons, including that they often arise in practice, as solution sets of equations ( elaborated above by the fact that algebraic varieties, analytic varieties, etc.

can be stratified into manifold pieces ), and that they are the space " modeled on " Euclidean space ( a space that looks locally like Euclidean space ) – i. e., they arise naturally when considering subsets and quotients of Euclidean space.