prove that the quotient space obtained by identifying the points on the southern hemisphere, is homeomorphic to the whole sphere.I am trying to define a homeomorphism between the quotient space and the sphere,and i need help doing it.
Thank's in advance.
how can i show that the matrix logarithm log(I+A) is continuously differentiable on the set of matrices having operator norm less than 1.
The Attempt at a Solution
i tried to compute the...
Using the definition of Hausdorff measure:
I am looking for a simple proof that Hd(C) is greater than 0, where C is the Cantor set and
Thank's in advance
I am trying to understand why do the two versions of Hausdorff (fractal) dimension are actually the same.I refer to the definition by coverings and the definition by ratio of two logarythms.