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Results tagged with gn.general-topology
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user 124004
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
6
votes
Accepted
Is the dimension given by Klee trick ever sharp?
Are the embeddings required to be isometric embeddings? If not, then what about including three points into $\mathbb{R}$ in two ways, so that the middle point of the three changes? More explicitly, …
- 3,451
6
votes
Cover the $n$-disc irredundantly with $n+1$ open sets. Suppose that the $(n+1)$-fold interse...
It is not true in general. Let $n=3$, and take a piece of a brick wall (thickness one brick) that is homeomorphic to a 3-disc. For example, just take a largish rectangular wall. There are bricks of …
- 3,451
12
votes
Accepted
Quotient of solid torus by swapping coordinates on boundary
Your quotient manifold is homeomorphic to $S^3$. I know this because it is a closed 3-manifold and its fundamental group is trivial, so I'm quoting the Poincare conjecture/Perelmann's theorem. The f …
- 3,451
0
votes
How can I construct a closed manifold from a finite CW complex?
The mod-2 homology groups of any closed $n$-manifold are `$n$-palindromic' by Poincare duality, i.e., $H_m(M;\mathbb{Z}/2)\cong H_{n-m}(M;\mathbb{Z}/2)$ for each $m$. If the mod-2 homology of $X$ is …
- 3,451