Definition talk:Manifold

Not sure whether disambiguation is what you need to distinguish between Differential, Smooth and Complex manifolds, although Linear Manifold may be different in concept. All these are basically the same sort of thing. Disambiguation should be used for things which are genuinely different concepts, like connectedness on topological spaces is different from that on graphs. As such, perhaps we need "Manifold (Topology)" with the three subconcepts added as "also see", or perhaps manifold with three transcluded subpages. This disambig would then be reduced to two different concepts: one for topology and one for linear algebra. --prime mover (talk) 23:00, 30 November 2012 (UTC)

I agree, in particular I think manifold with three (in fact four: $\mathcal C^0$-manifolds should definately have their own definition) transcluded subpages is a good way to do it.

In fact, it seems the definition of a linear manifold is a little awkward to place. Some people (e.g.) have a linear manifold defined as manifold with a natural vector space structure. PlanetMath here have it as an affine space with it's natural manifold structure (i.e. in reverse, but the same thing).

The terminology is used by Paul Halmos; so is probably justified, but it leaves open the question of whether a linear manifold should be presented as a special case of a manifold. --Linus44 (talk) 11:14, 1 December 2012 (UTC)

Okay then, let me have a go at refactoring - I'll see what I can do ... --prime mover (talk) 12:38, 1 December 2012 (UTC)

So far so good. Our implementation of this field of mathematics still has plenty of scope for enhancement. --prime mover (talk) 13:28, 1 December 2012 (UTC)

@Linus44: Interesting. It cannot be the case in full generality however, because a linear manifold may not be closed (in fact that's the reason for the terminology in the first place) and furthermore may have infinite dimension, and I'm fairly sure that latter cannot be repaired. --Lord_Farin (talk) 18:17, 1 December 2012 (UTC)