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network profile
| bio | website | |
|---|---|---|
| location | ||
| age | ||
| visits | member for | 4 months |
| seen | Mar 23 at 10:46 | |
| stats | profile views | 30 |
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Feb 7 |
accepted | Urysohn Metrization Theorem: show that $F$ is continuous. |
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Feb 6 |
comment |
Urysohn Metrization Theorem: show that $F$ is continuous. With $f(y) = \sum_{n=1}^{\infty} \frac{f_n(y)}{n}$, you're referring to some Urysohn function $f:X\rightarrow [0,1]$? Or the embedding $F:X\rightarrow H$? I am guessing the latter, but then what do you mean with the sum of all Urysohn functions $\frac{f_n}{n}$? Because, $F(y) = \left( f_1(y), \frac{f_2(y)}{2}, \frac{f_3(y)}{3}, \dots\right)$? Or am I seeing thing the other way around.. |
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Feb 6 |
comment |
What are relative open sets? @DanielRobert-Nicoud - D'oh! I meant to prove that $F$ is open. Indeed.. But then, it is the same to find $F(W)$ open as to find $F(W)$ as the union of relatively open sets? |
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Feb 6 |
revised |
Having a tough time finding the area between two curves. added 173 characters in body |
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Feb 6 |
answered | Having a tough time finding the area between two curves. |
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Feb 6 |
comment |
What are relative open sets? @DanielRobert-Nicoud - In Urysohn's Metrization Theorem we have some space X and construct a function $F: X \rightarrow H$, where $H$ is the hilbert cube. The idea is then to show that $F$ is an embedding by proving $F$ to be one-to-one, continuous and open. When proving continuity let $W$ be open in $X$, then they show that $F(W)$ is the union of relatively open sets. So normally when proving continuity one would need to find an open $F(W)$, but here they suffice with the union of relatively open sets. |
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Feb 6 |
comment |
What are relative open sets? @Daniel Robert-Nicoud - Suppose I want to prove something, e.g. continuity, such that I would need to find some open set $U$. Would it be sufficient to show that there exists a relatively open set? |
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Feb 6 |
accepted | What are relative open sets? |
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Feb 6 |
asked | What are relative open sets? |
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Feb 6 |
asked | Urysohn Metrization Theorem: show that $F$ is continuous. |
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Feb 4 |
accepted | Urysohn's Metrization Theorem: What is needed to show that $F$ is an embedding? |
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Feb 4 |
comment |
Urysohn's Metrization Theorem: What is needed to show that $F$ is an embedding? So it is the same as to say that $F$ is a continuous bijection? An open mapping corresponds with an continuous inverse function if I'm not wrong. |
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Feb 4 |
revised |
Urysohn's Metrization Theorem: What is needed to show that $F$ is an embedding? added 1 characters in body |
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Feb 4 |
asked | Urysohn's Metrization Theorem: What is needed to show that $F$ is an embedding? |
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Feb 4 |
accepted | Open mappings and continuous functions? Are these interrelated? |
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Feb 4 |
asked | Open mappings and continuous functions? Are these interrelated? |
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Feb 2 |
accepted | Trying to understand Hilbert Spaces… |
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Feb 2 |
comment |
Trying to understand Hilbert Spaces… @julien. Aha, so a Hilbert space need not to be infinite? How can i get more info on $\ell^{2}(\mathbb{R})$? What is this space called? |
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Feb 2 |
asked | Trying to understand Hilbert Spaces… |
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Jan 31 |
accepted | Every $T_3$ space with a countable basis is $T_4$. |
