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Results tagged with gn.general-topology
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user 5952
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
13
votes
Are the rationals homeomorphic to any power of the rationals?
Yes, they are homeomorphic. To construct a homeomorphism from $\mathbb Q$ to $\mathbb Q^2$, one can proceed roughly as follows: express $q\in \mathbb Q$ as a continued fraction $[a_0, a_1,a_2,...]$ (o …
- 4,015
41
votes
Applications of connectedness
You can use conectedness of $\mathbb R^n \setminus 0$ for $n\geq 2$ to show that doesn't exist a an $\mathbb R$-division algebra of any odd dimension $n\geq 3$.
Take any odd $n\geq 1$ and a $\mathbb …
11
votes
Accepted
Two Definitions of "Character" of topological groups
I am assuming all groups we are talking about are locally compact and commutative.
The two definitions indeed do ageree on profinite groups. To prove it, you have to check that the functors $Hom(-,\m …
- 4,015