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Mar
24
comment $E$ compact, real-valued $f : E \to \mathbb{R}$ continuous iff graph is compact - is real valued necessary?
@SantiagoCanez. You're right. $g^{-1}$ is clearly continuous as it's the restriction of a projection map on the first coordinate, but this detail is essential in order to conclude the continuity of $g$ given the other assumptions.
Mar
24
answered Are $l^p$ spaces compact?
Mar
24
comment infinite Union of compact sets
@pratik: Each $I_{n}$ is compact. But is $\mathbb{R}$ compact?
Mar
24
answered infinite Union of compact sets
Mar
24
comment $E$ compact, real-valued $f : E \to \mathbb{R}$ continuous iff graph is compact - is real valued necessary?
Can you elaborate why in the second direction of your proof: $g$ is continuous knowing that $G$ is compact and $g$ is bijective? This doesn't seem right.
Mar
19
revised Compact Projections to $S^1$
added 190 characters in body
Mar
19
comment Compact Projections to $S^1$
$\mathbb{R}^{2}$ is certainly not compact.
Mar
19
answered Compact Projections to $S^1$
Mar
19
awarded  Popular Question
Mar
12
answered Countability of certain subset of $\mathbb{R}$
Mar
12
comment what can you conclude about the number of solutions of the linear system Ax = b?
Why would $A$ have a right inverse? It could be that $a_{1},...,a_{4}$ span something lower dimensional that $\mathbb{R}^{3}$. In fact $A$ could be anything from the null matrix to full rank matrix here.
Mar
12
comment If $\| f \|_p \leq 1$, then $|f(x)| \leq 1$ for some $x$
Yeah, that would do the job.
Mar
12
comment what can you conclude about the number of solutions of the linear system Ax = b?
@sovon: Which part did you not understand?
Mar
12
comment If $\| f \|_p \leq 1$, then $|f(x)| \leq 1$ for some $x$
@kobe: If $f>g$ then in general $\int f\geq \int g$. The pointwise consideration is not taking in to account any properties of the measure and the integration depends on the measure. I guess his question is how do you conclude here that the inequality is strict with the integrals? Might be trivial in the case of Lebesgue measure, but what is the argument?
Mar
12
revised what can you conclude about the number of solutions of the linear system Ax = b?
added 98 characters in body
Mar
12
comment what can you conclude about the number of solutions of the linear system Ax = b?
@YourAdHere: If you assume that $a_{1},...,a_{4}$ are the columns of $A$, then yes. But in that case there are infinitely many solutions as I pointed out.
Mar
12
answered what can you conclude about the number of solutions of the linear system Ax = b?
Mar
12
comment what can you conclude about the number of solutions of the linear system Ax = b?
What do we know about $a_{1},...,a_{4}$? Are those the columns of $A$?
Mar
10
comment A doubt in Probability essentials by Protter
@user3503589: You're welcome.
Mar
10
comment A doubt in Probability essentials by Protter
@jdods: $X$ is an indicator function in part $(v)$ and this seems to be a discontinuation of it, and rather a general statement. In either case it makes no difference, if one leaves the absolute values the argument goes through with same steps.