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Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.

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 …
Klaas's user avatar
  • 181
7 votes
1 answer
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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 …
Klaas's user avatar
  • 181