Manifolds

Sometimes I click around Wikipedia just for the hell of it. That's how I wound up with that lovely (?) schematic of Xenon. Well, today I went through the mathematics "portal" and found that the highlighted article was about manifolds. And I "learned":

A manifold is an abstract mathematical space in which every point has a neighborhood which resembles Euclidean space, but in which the global structure may be more complicated.

Got that? The global structure may be more complicated than one in which every point has a neighborhood "which" (I think they mean "that") resembles Euclidean space.

Postscript: To clarify, I don't actually read the Wiki articles. I just like to look at the pictures . . . and to remind myself of just how breathtaking the scope of my ignorance is.