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Jan
8
answered Characterisation of compact subsets of Banach spaces
Jan
8
revised Is the space $C[0,1]$ complete?
Suggestion in comment implemented.
Jan
8
revised Is the space $C[0,1]$ complete?
Proof of uniform limit theorem added.
Jan
8
revised Is the space $C[0,1]$ complete?
Part (iii) added.
Jan
8
revised Is the space $C[0,1]$ complete?
Additional note and link to related post added.
Jan
8
comment Is the space $C[0,1]$ complete?
I'm a bit late with this answer but I thought I'd add something slightly more general. Seeing as there are already two answers you may ignore me. : )
Jan
8
answered Is the space $C[0,1]$ complete?
Jan
8
revised Space of bounded continuous functions is complete
Notation corrected.
Jan
8
revised Space of bounded continuous functions is complete
Notation corrected.
Jan
7
comment How to prove $C_1 \|x\|_\infty \leq \|x\| \leq C_2 \|x\|_\infty$?
@Fabian Nice : ) Thank you!
Jan
6
comment implementation of xnor with lambda
Have you seen this?
Jan
5
comment How to prove $C_1 \|x\|_\infty \leq \|x\| \leq C_2 \|x\|_\infty$?
I personally find it slightly confusing to use $n$ as an index variable to sum over if $n$ also denotes the dimension of the space.
Jan
5
comment How to prove $C_1 \|x\|_\infty \leq \|x\| \leq C_2 \|x\|_\infty$?
@Fabian: Assuming that $\| x \|_\infty := \max_{i \in \{1, \dots , n\} } x_i$ I think you are missing an $n$ in the following line: $$ \| x - y \| = \dots \leq n \| x - y\|_\infty$$
Jan
4
revised Finding limit for the function
One brace deleted.
Jan
4
revised $C_c(X)$ dense in $L_1(X)$
added 38 characters in body
Jan
3
comment $C_c(X)$ dense in $L_1(X)$
Dear @MattE, thanks for pointing this out. I think it's fixed now.
Jan
3
revised $C_c(X)$ dense in $L_1(X)$
Different version of Tietze added as discussed with tb to fix mistake pointed out by MattE.
Jan
3
answered $C_c(X)$ dense in $L_1(X)$
Jan
3
comment Picard's method application
I assume you meant to write "on which interval".
Jan
3
answered Smooth functions with compact support are dense in $L^1$