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Results tagged with examples
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user 238
For questions requesting examples of a certain structure or phenomenon
3
votes
2
answers
437
views
What is a good example of a hyperspace where the base space is non-Hausdorff?
Let $X$ be a topological space, and let $\operatorname{CL}(X)$ be its hyperspace. That is, $\operatorname{CL}(X)$ is the set of closed subsets of $X$, equipped with the minimal topology so that the ca …
- 8,532
4
votes
Examples where Kolmogorov's zero-one law gives probability 0 or 1 but hard to determine which?
I can't seem to reply to Martin's response so I'm making a new one.
The first question one asks in percolation theory is whether an infinite open cluster exists. The zero-one law applies because as …
- 8,532
4
votes
3
answers
3k
views
Examples of Banach spaces and their duals
Is there a book or survey article with a rich set of examples?
Here is the particular example which motivates this question. …
- 8,532
3
votes
3
answers
918
views
A non-trivial probability measure on $2^{\mathbb R}$
Consider the measurable space $2^{\mathbb R}$, equipped with the tensor-product $\sigma$-algebra. Famously, this space has a measurable structure which is not generated by a topology (see this answer) …
- 8,532
5
votes
1
answer
468
views
Measures which exhibit the "uncorrelated implies independent" property
I am hoping there are some interesting examples of non-Gaussian UII measures with infinitely many degrees of freedom. If they do not exist, I will be very interested to see the proof. …
- 8,532
17
votes
7
answers
1k
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Examples of toposes for analysts
I've read that toposes are extremely important in modern mathematics, but I find the definitions and examples given on the nLab page a little too abstract to understand. … Can you provide some examples of toposes which are of use to analysts? e.g., toposes where the objects consist of topological spaces, measure spaces, etc. …