Recent content by Jooolz

Thank you so much! :-) Do you possibly know why it now follows that the multiplier ring of the ideal is not equal to $\mathbb{Z}[\sqrt{-19}]$? And that the ideal is not invertible?

Thank you very much for your help. but i get stuck with this kernel($f$)= {$a + b\sqrt{-19} : f(a+b\sqrt{-19})=0$} = {$a+b\sqrt{-19} : a -b \pmod2 $}={$a+b\sqrt{-19} : a=b \pmod2 $} I am missing something crucial here cause i just don't understand why this is equivalent to the ideal $(2...

hello all of you Why is (2, 1+sqrt(-19)) a maximal ideal of Z[sqrt(-19)]? How to show such thing? I thank you for any hints

thank you. "For the reverse, just construct a counterexample. Take the plane and consider the function f(x,y)=arctan(x2y2)" Would g-1((-∞, b)) be open if Y is a compact space?

or is it the set were t + ε/2 < f(x,y) < t + ε ?

Hi zhentil, Thank you very much for helping! Sorry, I don't see immediately why this holds: "By definition of continuity, there exists an open set A containing (x,y) such that f(x,y)>t+ϵ/2 for all (x,y)∈A" For this we need that some subset of { f(x,y) } is open?

Hi all, I am struggling with the following: If X and Y are topological spaces. and f: X x Y → ℝ is a continuous function (product topology on X x Y, Euclidean topology on ℝ) Let g: X → ℝ defined by g(x) = sup { f(x,y) | y in Y } Then: If A=(r, ∞) for r in ℝ, g-1(A) is open. And If...

Yes I've heard about Pn(ℝ), but I always try to avoid them... cause they're creeping me out... Well, I use a book/reader that is made by a professor of my university... And every now and then I skip through the pages of General Topology by Stephen Willard Do you know it?

Now you've made me cry... In my book they are saying that the one-point-compactification of the quotiënt space (S1 X ℝ)/~ Is in fact homeomorphic to the real projective plane... So of course I want to know why that is... pfffff... first I wanted to know what I am actually dealing with...

I was thinking of it this way: having the infinite cylinder standig so that the height is the z-axis... and then a point of a circle would be (x, y, z) where z is the midpoint...Cause the height of points on the same circle would be the same... Wrong? So Am I... :-s

Of course... it is a cylinder :shy: Can you tell me if I'm thinking in the right direction with this: If we define an equivalence relation on S1 X ℝ by (x, t) ~ (-x, -t) Do they mean, that if we choose a point x on the cylinder (which is a point on a circle) the t would be...

thank you very much helping! :-) I don't think I really got it... So S1 x S0 = S1 x {-1, 1} ? with -1 and 1 on the x-axis? then draw two circles.. with midpoints (-1, 0) and (1, 0)? Or does it not make sense to talk about -1 and 1 on x-axis cause there actually isn't one...cause -1 and 1...

Hi all, I would really appreciate if someone can explain to me what is meant by a product of spheres. What would for example S1 x S0 look like? The first being a circle and the second being a pair of boundary points... So what kind of "object" is their product? And how about S1 x S1 or...

Hi all, Let λ>0 and define an equivalence relation on ℝn-{0} by (x~y) \Leftrightarrow (there is an s\inZ such that λsx=y) I would like to know what the quotient space ℝn-{0}/~ looks like. I know that it is a set of equivalence classes. To understand it better I wanted to see how it...