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14h
revised Algebra: What does “is defined for” mean?
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14h
reviewed Approve suggested edit on Algebra: What does “is defined for” mean?
14h
comment Finding the Upper Limit of A Function
What have you tried? Don't post homework questions without showing some effort. It's just going to get closed for being off-topic.
14h
revised Finding the Upper Limit of A Function
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1d
comment $L^{\infty}(G)$ as a Banach $L^{1}(G)$-bimodule. (Check my logic please!)
Don't use \bf in math mode for bold text. The StackExchange network uses Markdown for formatting text. Furthermore, don't use eqnarray.
1d
revised $L^{\infty}(G)$ as a Banach $L^{1}(G)$-bimodule. (Check my logic please!)
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2d
answered If there are obvious things, why should we prove them?
2d
comment Check continuity of linear functionals and find norms
Another way to see discontinuity of the first map is to note that it takes the bounded set $\{x_n \mid n \in \mathbb N\}$ to the unbounded set $\mathbb N$.
2d
revised Check continuity of linear functionals and find norms
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Apr
17
revised Continuous compactly supported real valued functions on a locally compact and $\sigma$ compact space is separable
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Apr
17
comment Continuous compactly supported real valued functions on a locally compact and $\sigma$ compact space is separable
I think "$\sigma$-locally compact" is a common abbreviation for "locally compact and $\sigma$-compact". I find it rolls off the tongue more easily.
Apr
17
comment Question about a closed subspace of a complete space
Isn't $K(J)$ just the ball of radius $\alpha$ around the function which is constantly equal to $x_0$? You hardly need to appeal to the definition of $d$. In any metric space it's the case that any closed ball is closed and any open ball is open.
Apr
16
comment Is a probability density function necessarily a $L^2$ function?
A slight correction: I think you need to divide $f$ by $2$ because you forgot a factor $2$ in the integral when computing $\|f\|_1$.
Apr
16
comment Fundamental Group of Klein Bottle?
$\mathrm{\LaTeX}$ tip: It's \mathbb{C} (or \mathbb C if you want to save a character): $\mathbb C$.
Apr
16
comment Topology - Product space example
You can drop Hausdorff-ness on $X$ and compactness on $Y$ and it's still true.
Apr
16
answered Topology - Product space example
Apr
16
comment Topology - Product space example
@HennoBrandsma same thing (in this case).
Apr
16
comment What does $g(f(x))=x$ imply?
For (c), I'm partial to the example $X = Y = c_c$ (q.v. sequence space) and the maps $S_R(x_1,x_2,\dotsc) = (0,x_1,x_2,\dotsc)$ and $S_L(x_1,x_2,\dotsc) = (x_2,\dotsc)$. Then $S_L \circ S_R$ is the identity, but neither is bijective nicely illustrating the difference between linear algebra in infinite dimensions and finite dimensions (which more or less boils down to a vector space being free on any of its bases and maps on finite sets being bijective iff they're in- or surjective).
Apr
15
comment topological equivalence on interior of $D^2$ that is not continously extendable to $D^2$
Oh. And after your latest edit which states that the basic open sets of $T_2$ are of the form $\{p \in \operatorname{int}(D^2) \mid \exists \epsilon {\color{red}\geq} 0 : B_\epsilon(p) \subseteq \operatorname{int}(D^2)\}$, $T_2$ is just the discrete topology which is probably not what you meant. And if you write "$>$" instead, it's the standard topology.
Apr
15
comment topological equivalence on interior of $D^2$ that is not continously extendable to $D^2$
He's saying that it's not a homeomorphism because the inverse $\operatorname{id}: (\operatorname{int}(D^2),T_2) \to (\operatorname{int}(D^2),T_1)$ isn't continuous.