Reputation
19,872
Next privilege 20,000 Rep.
Access 'trusted user' tools
Badges
8 48 131
Impact
~474k people reached

Jan
10
comment Looking for a proof of the completeness of $C^{n}[0,1]$.
@YemonChoi As for your last sentence in your last comment: I second that.
Jan
10
comment Looking for a proof of the completeness of $C^{n}[0,1]$.
@YemonChoi Yes, that's the uniform limit theorem. : )
Jan
10
comment Looking for a proof of the completeness of $C^{n}[0,1]$.
@YemonChoi The OP was not about $C^1([0,1])$ so this is not a "full" solution. As for general practice: I think a full solution is more helpful than a one liner pretending to be a hint. : )
Jan
10
comment Looking for a proof of the completeness of $C^{n}[0,1]$.
@YemonChoi The $n$-th derivative is continuous and bounded. Where would you use uniform continuity in the proof?
Jan
10
revised Pointwise convergence of a function
added 8 characters in body
Jan
10
revised Looking for a proof of the completeness of $C^{n}[0,1]$.
added 137 characters in body
Jan
10
answered Looking for a proof of the completeness of $C^{n}[0,1]$.
Jan
9
revised Characterisation of compact subsets of Banach spaces
deleted 30 characters in body
Jan
9
revised Characterisation of compact subsets of Banach spaces
deleted 62 characters in body
Jan
9
revised Characterisation of compact subsets of Banach spaces
deleted 4 characters in body
Jan
9
revised Characterisation of compact subsets of Banach spaces
Broken argument fixed as discussed with tb.
Jan
9
accepted Surface of genus $g$ does not retract to circle (Hatcher exercise)
Jan
8
revised Characterisation of compact subsets of Banach spaces
deleted 254 characters in body
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?