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Results tagged with gn.general-topology
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user 6153
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
21
votes
Accepted
How to understand the concept of compact space
Some heuristic remarks are helpful only to a subset of readers. (Maybe that's true of all heuristics, as a meta-heuristic - if everyone accepts a rough explanation, it's something rather more than tha …
- 12.6k
4
votes
Why are topological ideas so important in arithmetic?
If we think about Diophantine equations in general, the situation is "hopeless". That's a theorem. Nevertheless in number theory we want to study such equations, in special cases at least, so some ide …
- 12.6k
5
votes
Connections between ultrafilters in topology and logic
My feeling, which may be ignorant, is that these intuitions go all the way back to Leibniz. There "point" was in some way ridded of a silly definition like "position but no magnitude", and was replace …
- 12.6k
3
votes
A family of subsets with a "gluing" property
It's just an exercise in the transitivity of relations? You have the subsets where a given function F takes a given value: in other words any partition, or any equivalence relation. I wouldn't call th …
- 12.6k
4
votes
Compactification of a manifold
What do you want to do with an open annulus in the plane? Already open subsets of the plane may need infinitely many points added to compactify them in a sensible way.
- 12.6k