@user1 For example, to prove that a continuous function $f:[a,b]\to\Bbb R$ is regulated, I fix $\epsilon$ and define $P_\epsilon(y)$ to mean "There exists a step function $s:[a,y]\to\Bbb R$ such that $|f(x)-s(x)|<\epsilon$ for all $x\in[a,y]$" and the look at the set $$A=\{x\in[a,b]:P_\epsilon(x)\}$$
Actually it should be something like $P(f,\epsilon,y)$, yes?
@AlexanderGruber I was also considering proving that it is equivalent to a property on a functor between two categories and then verifying that property by induction on a well-ordered set of categories.
@Charlie Also: It's important to notice that there are a lot of roles in life. You don't need to be a professional russian ballerina, helping others to achieve that and thinking about new stuff is also important.
Just started reading "Algebra, ch0" and the function decomposition theorem is wonderful. I can already see it is going to be useful. Not sure if I will be able to pull my eyes away from ch0 to read any of the other books I have planned (not sure if that is good or bad).
@Gustavo Hah. Yah you might just be getting ahead of yourself.
@Gustavo I have been typing my answers (so far...) so If you would like I could send them to you I could, plus I love talking about math, so if you are ever working through it I am pretty sure I would be willing to discuss it.
Gustavo: I notice you haven't accepted any answers to your more recent questions; have you been unhappy with the answers? You can always edit a question, or comment below answers, if you'd like more clarification, or if the answers do not address some lurking doubt/question. — amWhyMar 4 at 14:53
I don't know why I would have? I wouldn't have knowing it was you, maybe I just didn't look closely at the "OP" user name (your name), since I have no worries about your acceptance rate...hmmmm
@Gustavo When new additions are released (I would think). If you are using the digital version (easily found online), I don't it's a legit one put out by the author so he probabably does not release a new digital version every time he fixes errors.
@Ethan Well what I said is not restricted to mathematics, also if you have access to a library (that has access to journal databases) there is normally an option to search only for peer reviewed articles.
@Ethan No problem. Try google scholar. If you find an article there that you can't get I can check if I have access through my library and I won't ;) send you the pdf of the article.
@Mike the stickiness where's off every monthish, so one of me or robjohn has to repin it every once-in-awhile
@Bageer unfortunately the room description does not allow inline links (it just puts down the whole url in text), which made the description very ugly
it is also not too unreasonable to ask that new users "see below" as suggested, or perhaps expect they can Ctrl+F the word "guidelines" if they don't look hard/cleverly enough
The problem is saying: With notation as in example 2.4, explain how any function $f:A \to B$ determines a section of $\pi_A$. $\pi_A$ is the projection and example 2.4 is a diagram with $A\times B$ and two projections coming off of it (to $A$ and to $B$). My thought is that a section is a right inverse $A \to A \times B$, so the image of the section could be the graph of $f$. Or in other words the function that makes the diagram commute.
I guess I am just not sure if that is what the question is actually wanting. So do you guys think it is a decent answer?
The more I think about it the more I think that is what the problem is wanting, but I am a little afraid I am missing something.
When I want to prove that the product topology on $\mathbb R^n$ with repsect to the euclidean topologies on every factor is the n-dimensional euclidean topology, is it enough to show that the norm on the product topology equals the euclidean norm?
@Montaigne You would have to define the norm and show that the topology has the open balls wrt this norm as a base, then it would be sufficient to show that this norm is the same as the euclidean norm.
@Montaigne I would show that the set of open balls wrt the Euclidean topology is a base for the product topology and then that the base given by the factors in the product topology is a base for the Euclidean topology.
Yes this is the way I would do it also, but I am inetersted in the "non-topological" approach. Do you know any reference where it is proved that the maximum norm is induced by the product topology
