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| bio | website | |
|---|---|---|
| location | Florida | |
| age | ||
| visits | member for | 6 months |
| seen | 10 hours ago | |
| stats | profile views | 80 |
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May 8 |
comment |
Looking for a differentiable function which behaves somewhat like $\min(x,1)$ This doesn't work for n odd. |
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Apr 19 |
comment |
Prove a square is homeomorphic to a circle You're correct, he did decide to use the interior. You do not have to establish an inverse directly in order to show that a function is a bijection. Moreover, I think what was meant is (as I said) that you don't have to find the inverse and prove that it's continuous. It follows from the above (or would if we were dealing with the closures of the spaces) |
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Apr 19 |
comment |
Prove a square is homeomorphic to a circle Cameron: it is a standard result that a continuous bijection from a compact space to a Hausdorff space is a homeomorphism. Both sets in the OP are closed, compact, and Hausdorff. So a continuous bijection implies a homeomorphism without having to find an inverse and prove it's continuous. |
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Apr 12 |
comment |
Measurable Functions - Constructing Examples The pointwise limit of a sequence of measurable functions is measurable. So your second one (if I'm reading it correctly) is impossible. |
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Apr 8 |
awarded | Promoter |
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Apr 7 |
revised |
Measurability of a certain set in Falcolner's Geometry of Fractal Sets added 304 characters in body |
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Apr 6 |
asked | Measurability of a certain set in Falcolner's Geometry of Fractal Sets |
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Mar 23 |
comment |
Countably monotone does not imply monotone and countably additive? You're looking for a set function which is countably subadditive but not countably additive? Try Lebesgue outer measure on the powerset of $\mathbb{R}$. It's countably subadditive but is not countably additive (in general). |
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Mar 16 |
answered | Proof by contradiction - help!? |
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Mar 16 |
comment |
Pushforward measure integral property What have you done so far? Try starting when $f$ is simple. |
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Mar 13 |
comment |
If x is rational, $x\ne 0$, and $y$ irrational, prove $x+y, x-y, xy, x/y$ and $y/x$ are all irrational. You need to show that $x +y$ is irrational if $x \neq 0$ is rational and $y$ is irrational; we assume $y$ is irrational. If it were the case that $x + y$ is a rational number, then $(x+y) - x$ would also be a rational number. But that's just $y$, which contradicts our assumption that $y$ is irrational. |
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Mar 12 |
comment |
If every compact set is closed, then is the space Hausdorff? The title and question are different. The title asks if every compact set is also a closed set, is the space Hausdorff. The question asks if every set is closed and compact, is it Hausdorff. Which do you mean? |
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Mar 10 |
comment |
Existence of the limit from the left of real distribution functions It follows from the fact that $f$ is nondecreasing. |
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Mar 10 |
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How can I define a function to show that $\{3^n\mid n\in\mathbb{Z}\}$ is countably infinite? Do you know that $\mathbb{Z}$ is countably infinite? If so it's straightforward. Let $f$ be a bijection from $\mathbb{N}$ to $\mathbb{Z}$. Then map each $n \in \mathbb{Z}$ onto $3^n$. Now compose. |
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Mar 8 |
revised |
$\mathbb{R}^S$ for finite and countable set $S$ added 144 characters in body |
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Mar 8 |
comment |
$\mathbb{R}^S$ for finite and countable set $S$ True, I was thinking about subsets of $\mathbb{N}$ when I said that. I'll edit accordingly. |
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Mar 8 |
answered | $\mathbb{R}^S$ for finite and countable set $S$ |
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Mar 4 |
comment |
Interpretation of functional equation of dedekind eta function Thank you I'm dumb :( |
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Mar 4 |
asked | Interpretation of functional equation of dedekind eta function |
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Mar 3 |
accepted | Improper integral evaluation |
