Reputation
19,548
Next privilege 20,000 Rep.
Access 'trusted user' tools
Badges
8 47 125
Impact
~452k people reached

Oct
20
comment Sequence of bounded linear functionals on $C^1[0,1]$ that shows Principle of Uniform Boundedness fails without completion.
Why "hint"? I consider this a full answer.
Oct
20
comment $X,Y$ are Banach spaces, $T$ is linear, $x_n\to 0$ and $Tx_n\to y$, then $y=0$ and $T$ is continuous.
I don't understand the stuff after "Then, ...": you seem to be showing that $y=0$ but that is one of the assumptions.
Oct
20
comment Show that the directional derivative is linear by definition
I'm sorry but could you help me understand this? What I understand so far: In higher dimension the definition of the derivative involves a matrix so it is linear. On the other hand, the directional derivative does not seem to include such a matrix. Why does it nonetheless follow from the definition of directional derivative that it is linear? Thanks a lot in advance.
Oct
19
comment Partitions without 2
Not as active as before: Even with 50% activity you'd still be one of the more active users. Is less activity due to less interesting questions? Or is it my imagination that there are less interesting questions compared to 3 years ago?
Oct
16
comment Proof of that there is no metric on $\mathbb{R}$ which is equivalent to the natural metric and which induces a metric on $(0,1)$
Please can you provide your definition of when two metrics are equivalent?
Oct
15
comment Meaning of a discrete topological sub-space?
@Eric_ Yes, that's right. And sorry, I couldn't make sense of it before.
Oct
15
comment Meaning of a discrete topological sub-space?
Duh, beat me by 52 seconds and I didn't even get a notification that someone else posted an answer.
Oct
14
comment Density of sets
@learningmaths I see you got an answer along the same vein from Yiorgos so I'll assume your question has been answered to your satisfaction. There's nothing I can add : )
Oct
14
comment Density of sets
I have to leave my keyboard right now and I might add an answer to the second question when I return.
Oct
14
comment Density of sets
+1 for providing a question I like thinking about.
Oct
11
comment Metric topology induced by the sum of two metrics
Yay! You're back. Cool.
Oct
9
comment Follow up on a previous question of mine (characters in star algebra)
@MartinArgerami True but I still don't understand what's going on here. Concretely, what is OP doing wrong in the proof in the question? In the question the C star algebra is not zero so you can pick any non-zero element $a$ and use that $r(a^\ast a) = \|a^\ast a\|>0$, no?
Oct
9
comment Follow up on a previous question of mine (characters in star algebra)
Also every proper modular ideal is contained in a maximal ideal so even if there is no $1$ it seems plausible that maximal ideals exist. (?)
Oct
9
comment Follow up on a previous question of mine (characters in star algebra)
Please could you enlighten me as to what's going on here? It's a theorem in Murphy's book (see thm. 1.3.4. on page 14) that in a non-unital abelian Banach algebra $A$ we have $\sigma (a) = \{\tau (a) \mid \tau \in \Omega (A)\} \cup \{0\}$, so surely there cannot be a counterexample. Thank you in advance.
Sep
1
comment Homology of disjoint union is direct sum of homologies
@Vrouvrou Sorry this is way too long ago and I think I never really understood Mayer-Vietoris, sadly.
Aug
18
comment Every subsequence of $x_n$ has a further subsequence which converges to $x$.Then the sequence $x_n$ converges to $x$.
What's the setting here? Metric spaces?
Jul
22
comment Showing that an inclusion is null homotopic
@t.b. It's funny. Reading this I barely recognise my old self from 4 years ago.
Jul
22
comment Group of Unitaries: Strong Continuity
@Freeze_S Yes. The only exception that comes to mind now is when you post a comment on someone else's post like e.g. this answer. Then the author will get notified of the comments whether they include pings or not. No problem!
Jul
21
comment Group of Unitaries: Strong Continuity
@Freeze_S Wonderful. Also note that unless you ping users with "@username" they won't get pinged and won't notice it if you replied. I only saw it because I came here to check.
Jul
21
comment Group of Unitaries: Strong Continuity
@Freeze_S So why is the downvote still there? I'm going to make a trivial edit in case you don't have enough privileges.