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Results tagged with gn.general-topology
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user 2672
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
-2
votes
2
answers
913
views
Can topologies induce a metric?
Let {X,T} be a topology, T the set of open subsets of X.
Definition: Three points x, y, z of X are in relation N (Nxyz, read "x is nearer to y than to z") iff
there is a basis B of T and b in B …
- 9,720
5
votes
1
answer
966
views
Can topologies induce a metric? (revised)
This is a revised version of a question I already posted, but which patently was ill posed. Please give me another try.
For comparison's sake, the axioms of a metric:
Axiom A1: $(\forall x)\ d(x,x …
- 9,720
5
votes
3
answers
530
views
Probing a manifold with closed curves
Since fedja's excellent comment on Joseph's question on probing a manifold with geodesics remained uncommented (especially by topologists), I'd like to make a question out of it:
Conjecture: Given …
- 9,720