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Results tagged with gn.general-topology
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user 6514
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
25
votes
Accepted
A question about connected subsets of $[0,1]^2$
A counterexample to this statement was posted as a comment by Dejan Govc to the Math StackExchange question, Do partitions of a square into two sets always connect one pair of opposite edges?.
For $0 …
- 8,483
26
votes
Can non-homeomorphic spaces have homeomorphic squares?
Yes. Let $M$ be the Whitehead Manifold, which has the property that $M \not\cong \mathbb{R}^3$, but $M\times\mathbb{R}^3 \cong \mathbb{R}^6$. (In fact $M\times\mathbb{R} \cong \mathbb{R}^4$.) Let
$$ …
- 8,483
7
votes
Accepted
Extending a map from $S^n\to M^n$ to a nice map from $B^{n+1}\to M^n$
The answer is no, essentially since higher homotopy groups of spheres are nontrivial.
For example, in the $n=3$ case let $M=B^3$ and let $\sigma\colon S^3 \to M$ be the Hopf map from $S^3$ to the bou …
- 8,483