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5
questions
0
votes
1
answer
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Modifying the density of the real line
I am having issues trying to do something that is fairly simple. Given the interval [0,1] I need to find a function from [0,1] to [0,1] that concentrates the point density around $x=0.5$.
So for ...
- 3,439
0
votes
1
answer
38
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Class $C$ functions
How do you prove the following:
In general, a $C^k$ function is contained in $C^{k-1}$ for any $k$.
Why is this true? Thanks for helping.
- 5,164
8
votes
2
answers
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Info on the locale of surjections from the Natural Numbers to the Real Numbers
On the nlab page for locales, it states that there is locale for the surjections from the Naturals to the Reals. This locale has no points (i.e. elements), since there are no such surjections, but the ...
- 10.5k
1
vote
1
answer
39
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For $f(x, y) = x-y$, is $f(K \times K)$ closed if $K$ is closed?
$f: \mathbb{R}\times \mathbb{R} \rightarrow \mathbb{R}$ such that $f(x, y) = x-y$. For $K \subset \mathbb{R}$ closed is $f(K\times K)$ closed?
For the closed interval this is straight forwardly true ...
3
votes
2
answers
160
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Is the function $\,f(x, y) = x-y\,$ closed?
Is the function $\,\,f: \mathbb{R}\times \mathbb{R} \rightarrow \mathbb{R}$, defined as $$f(x,y)=x-y,$$ closed?