Recent content by felper

The converse is useful to verify if some topological space is metrizable: if it's not a Hausdorff space, it can't be metrizable.

Note that the function \dfrac{1}{1+x} is increasing on R+.

The way you "measure space-time" is the same as you measure the length of curves on a surface: you integrate the tangent vectors along the curve. your course is about manifolds? if you have a manifold, the metric gives you a way to measure the metric properties of the tangent plane. So, if you...

Read about this http://en.wikipedia.org/wiki/Integral_equation

the angle you seek, is the angle between the tangent vectors of the end of each side of the triangle

\mathrm df(p) is onto its image. Also, if you think f(U) as a manifold, its totally clear it's tangent space is R^n.

Note that \mathrm df(p) is a linnear transformation between vectorial spaces. The tangent space to R^n at p is R^n. The tangent space to f(U) at f(p) is again R^n, so, by Dimension Theorem, \dim(\ker(\mathrm df(p))=0, and then, \mathrm df(p) is inyective.

It looks interesting, what's the name of Burago's book?

Hi I think that you're a little confused: a set X with a function f:X\times X\rightarrow \mathbb{R}\cup \{0 \} holding triangular inequality, simetry and d(x,y)=0 \leftrightarrow x = y is called a metric space, and the function f is called metric. This in the analysis context. In the...

Thanks, i could demonstrate it. I'll think about the question.

look at thous links http://members.chello.nl/j.beentjes3/Ruud/catfiles/catenary.pdf http://www.sc.ehu.es/sbweb/fisica/solido/din_rotacion/catenaria/catenaria.htm the second one is in spanish, you can translate it :P

When you have to prove that a metric space is complete, the only space that we know that is complete, is R, so...

Remember that if you want to prove a sets equality, you have to prove both inclusions. En this case, there is a trivial inclusion (which?).

Let X be the quotient space obtained of \mathbb{R} identifiying every rational number to a point. Is X a Hausdorff space? Is X a compact space?

Hi there! Iam new in PF, iam very glad to know this place, so, i'll try to contribute and participate as much as i can (and as my english allows me haha). Now, is there a place to post proposed problems ? i'd like to share some beauty problems with the community, and a i want to do it in the...