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Results tagged with counterexamples
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user 61536
A counterexample is an example that disproves a mathematical conjecture or a purported theorem. For example, the Peterson graph is a counterexample to many seemingly plausible conjectures in Graph Theory.
4
votes
Accepted
Is there a Hausdorff weakly Lindelof space which is not DCCC?
The answer to this problem is negative because of the following
Theorem. If a topological space $X$ is weakly Lindelof, then each discrete (more generally, locally countable) family of open sets in $ …
- 41.8k
5
votes
Accepted
Hausdorff quasi-Polish spaces
I hope that the following space $P\mathbb Q^\omega$ is second-countable and quasi-Polish but not Polish.
Let $\mathbb Q$ be the field of rational numbners endowed with the discrete topology. Then its …
- 41.8k
12
votes
Accepted
If $\text{dim}(X \times X) = 2\text{dim}(X)$, does $\text{dim}(X^n) = n\text{dim}(X)$?
As John Samples noted in his comment, Dranishnikov's Theory of cohomological dimension implies the positive answer to this problem for compact (even $\sigma$-compact) metrizable spaces. Namely, accord …
- 41.8k