Hi,
I need help in proving the following statement:
An abelian,transitive subgroup of the symmetric group Sn is cyclic,generated by an n-cycle.
Thank's in advance
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.
If all columns of a matrix are unit vectors, the determinant of the matrix is less or equal 1
I am trying to prove this assertion,which i guess to be true.
can anybody help me?
Thank's in advance
I mean,continuously differentiable as an operator,that is, the derivative is continuous as a function of the matrix A.I will be glad if you send me a more specific hint.
Homework Statement
Hi,
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.
Homework Equations
http://planetmath.org/matrixlogarithm
The Attempt at a Solution
i tried to compute the...
Hi,
Using the definition of Hausdorff measure:
http://en.wikipedia.org/wiki/Hausdorff_measure
I am looking for a simple proof that Hd(C) is greater than 0, where C is the Cantor set and
d=log(2)/log(3)
Thank's in advance
Hi,
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.
http://en.wikipedia.org/wiki/Hausdorff_measure...
Hi,
Can someone give me a link to a clear and relatively basic and short matirial introducing the notion of fractal dimension (Hausdorff dimension)?
Thank's in advance.
Hi'
can the rational numbers be imbedded in a countable complete metric space X?
If D is the set of isolated points of X,then D is dense in X\D is countable complete metric space so it is homeomorphic to Q.Where am i wrong?
Hi,
I am trying to prove that any compact metric space that is also locally connected,must be locally path connected.
can someone help?
thank's in advance.
Homework Statement
It is clear that a countable complete metric space must have an isolated point,moreover,the set of isolated points is dense.what example is there of a countable complete metric space with points that are not isolated?
Homework Equations
The Attempt at a Solution
I mean that there exists a basis for the topology consisting of clopen sets.
I tried to find such basis using the compacity and properties of connected components,so far without results.I need some hints.
The number of connected components need not be finite.consider the cantor set.Also for x~y why does it have to be the same set that is both connected and clopen that includes x and y?
Thank's
Homework Statement
X is a compact metric space, X/≈ is the quotient space,where the equivalence classes are the connected components of X.Prove that X/ ≈ is metrizable and zero dimensional.
Homework Equations
Y is zero dimensional if it has a basis consisting of clopen (closed and open at...
if we consider ,instead ,the rectangle −M≤Rez≤M ,- 2mπi≤Imz≤2nπi for large M and integers m and n,then the image would be a new rectangle around the origin,transversed possibly several times.Is it true that it is transversed m+n times?