Novicorp WinToFlash Professional 1.5.0000 Portable
Novicorp WinToFlash Professional 1.5.0000 Portable
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Determine if this space is complete
Let $T_r = \{(x_1,…,x_n) \in \mathbb{R}^n: \sum_{i=1}^n x_i = r\}$ and $T_\infty = \{(x_1,…,x_n) \in \mathbb{R}^n: x_i \in \mathbb{R} \ \forall i\}$. Find the dimension of $T_r$ and $T_\infty$
The answer I have is $T_\infty = \mathbb{R}^n$ and $T_r$ has dimension $r-1$
I have to solve it by finding a subset of $T_\infty$ that is dense and show that this subset is uncountable. What I tried is, $T_\infty$ is complete and $T_r$ is a closed and bounded subset, so $T_r$ is complete. How would I show that this set is dense?
A:
The set is dense. Let $\{(x_n\}_n\subset T_r$ and $x\in T_\infty$. Then $x_n\to x$ as $
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