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Results tagged with gn.general-topology
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user 132128
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
7
votes
1
answer
501
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Topology of connected subsets of the $3$-torus
Consider the $3$-torus $Y=T^3$, a subset $\Sigma\subset Y$, and $\Sigma^*=Y\setminus\overline\Sigma$.
We assume both $\Sigma$ and $\Sigma^*$ to be open, connected, and smoothly bounded.
I am concerne …
- 181
1
vote
Topology of connected subsets of the $3$-torus
The following is my own attempt at an answer. I would appreciate critical proofreading.
The exact sequences of the pairs $(Y,\Sigma)$ and $(Y,\Sigma^*)$ show that
$$
A=\operatorname{im}(i^*:H^1(Y,\Si …
- 181