Talk:Topology Glossary
From Math Images
Htasoff 21:26, 2 July 2011 (UTC) Some topics that I'm not sure should or shouldn't be included;
- Basis
- Neighborhood
- Normal
- Homotopy
- Connected
- simply
- hyper
- etc.
- Isometry
- Isomorphism
- Local
- Locally (insert property here)
- Metric
- Products/ Quotients
Notes
| Bounded: limit exists to how far points can get from each other | |||
| Edge not included | Edge included | No edge | |
| Closed-ness | Note closed | closed | closed |
| compactness | not compact | compact | compact |
| Manifold-ness | Manifold | not manifold | manifold |
|}
Manifold: all neighborhoods are n-1 balls
Closed: included all of itself (includes boundaries if there are any.).
Compact = closed and bounded
Unbounded: no limit exists to how far points can get from each other
Boundary does not equal bounded
Kate 20:15, 17 June 2011 (UTC): I agree with Leah that if this is all you have to say, it might as well be a bubble in whatever page you're talking about. That said, I think there's more you can say - first of all, you should have some sort of visual example. Second, it might also be helpful to also explain it in terms of normal vectors.I found that discussing normals to the surface confuses the matter, because it introduces a direction not on the manifold. This may keep people from being able to visualize an object within the manifold, rather than merely on top of it. I'm also reluctant to talk about bases because many people will not be familiar with the concept.
Leah A bubble of manifolds should be included, I think. You're introducing a term not many people are familiar with. Also, now that I'm thinking about it, if the definition is about two sentences max then maybe this page isn't necessary. Maybe the future pages that would link to this could just include a short definition and how the definition alters/arises for a particular surface. That's unless you are going to expand this page by including a demo or whatever.
