Reputation
3,566
Top tag
Next privilege 5,000 Rep.
Approve tag wiki edits
Badges
8 32
Newest
 Custodian
Impact
~28k people reached

9h
comment What is $1+2+4+8+16+…+2^n$?
Neat.$\text{}\text{}$
1d
comment Prove Euler characteristic is a homotopy invariant without using homology theory
A professor of mine once defined the Euler Characteristic of surfaces using triangularizations (which is essentially CW-complexes), then argued that one couild prove that the EC was not dependent on the triangularization by refining two triangularizations to a third one and showing that the EC "agreed" on the refining. Maybe this idea gives some clue on how to solve your question (I really don't know if it does, since I never tried to do it because homology is quite powerful and solves the issue beautifully enough)
1d
comment Is there some connection between the killing form and a killing vector field?
Yes, apart from that : P
1d
asked Is there some connection between the killing form and a killing vector field?
Aug
22
comment Limit of definite integral of $f(x)\cos(mx)$
OP, go to baby Rudin pg. 188. I think that it may be the best place to find an answer that suits your needs. You can even find almost exactly the question you are asking in pg. 190, line 3.
Aug
22
comment Limit of definite integral of $f(x)\cos(mx)$
Although a correct answer, OP states explicitly: "This exam assume no knowledge in measure theory and Lebesgue integral."
Aug
22
comment Limit of definite integral of $f(x)\cos(mx)$
Hint: Bessel Inequality
Aug
22
answered Is $lim_{x \to a}\int_{g(x)}^{h(x)}f(t)dt$, where $g(a) = h(a)$, always equal to $0$?
Aug
12
answered Alternative to dense subsets for non-Hausdorff spaces
Aug
11
reviewed Close compact set problem
Aug
11
reviewed Close When has one sufficiently mastered an area of mathematics?
Aug
11
reviewed Approve Continuity & topology question
Aug
11
answered $\frac{7}{5} \equiv 11 \pmod{12}$. Why is it $11$?
Aug
11
comment Why are the fundamental theorems of calculus usually associated to the Riemann Integral?
That is not my intention at all. There is far more for measure theory than the lebesgue measure. Now, as a comparison, it is common practice (at least in my country) to sometimes do Real Analysis without constructing $\mathbb{R}$ explicitly (with dedekind cuts or etc). I don't think it is unreasonable to do the same with the Lebesgue Measure and integration. Furthermore, maybe I aggree with you about calculus. But in calculus, even riemann integration is not done properly. I'm talking about the majority of introductory real analysis books and courses, not calculus.
Aug
11
answered The Fundamental Theorem of Calculus (for the lebesgue integral)
Aug
10
comment Open connected subsets of path-connected spaces
As an observation, note that the assumption of locally path-connectedness on $X$ would imply a positive result: since then you would be able to prove that a path-connected component of $Y$ would be both open.
Aug
10
comment Open connected subsets of path-connected spaces
Not equivalent, but related: math.stackexchange.com/questions/766422/…
Aug
10
answered Every open set in the real line is the countable union of disjoint intervals
Aug
10
comment Gluing diagrams: is it possible to glue a surface with itself in the same point? how is the diagram drawn?
Hmm... I'm not sure if I understood your question correctly then. Could you please elaborate more what you mean by "glue the surface with itself in the same point?".
Aug
10
answered Gluing diagrams: is it possible to glue a surface with itself in the same point? how is the diagram drawn?