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Results tagged with gn.general-topology
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user 8962
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
4
votes
Pair of curves joining opposite corners of a square must intersect---proof?
A homological proof would use the intersection form of the torus. if you consider these paths as based loops on the torus, you see that they are represented as (1,1), and (1,-1), in terms of the stand …
- 111
7
votes
Pair of curves joining opposite corners of a square must intersect---proof?
This is a really interesting question. But it only involves basic homotopy theory, not anything as subtle as the Jordan curve theorem.
Proof:
Let the paths be parameterized as $v(t)$, and $w(s)$, $t …
- 111