# Search results

1. ### Transitive subgroup of the symmetric group

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

Thank's
3. ### Quotient space of the unit sphere

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.
4. ### The box topology on R^ω

I am trying to show tha the coorinates Xn,m=X0,m for n and m greater from som M and N.(where Xn converges to X0 in the box topology)
5. ### The box topology on R^ω

Hi, What are the convergent sequences in the box topology on R^ω?Are they the eventually constant only? Thank's in advance
6. ### Determinant of a unit columns matrix

You mean to decomposite the euclidean space to direct sum ,using torthogonal space of each vector? If not,can you specify more?
7. ### Determinant of a unit columns matrix

Yes,i know that but i am searching for a proof.
8. ### Determinant of a unit columns matrix

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
9. ### Matrix logarithm

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.
10. ### Matrix logarithm

And how do i do that?
11. ### Matrix logarithm

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...
12. ### Hausdorff dimension of the cantor set

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
13. ### Fractal (Hausdorff) dimension

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...
14. ### Fractal (Hausdorff) dimension

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.
15. ### Imbedding of the ratiomals

But Cauchy sequence in Q may not be Cauchy in the complete space.Homeomorphism preserves the topology,not the metric.
16. ### Imbedding of the ratiomals

why,beacause the imbedded image must be closed hence topologically complete?Why does it have to be closed?
17. ### Imbedding of the ratiomals

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?
18. ### Product space

Is there atopological space X such that XxX (the product space) is homeomorphic to the unit circle in the plane
19. ### Locally path connected

hahn mazurkiewicz theorem gives the answer
20. ### Locally path connected

You mean to show that this is clopen?This is my difficulty.I suppose the compacity is needed
21. ### Locally path connected

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.
22. ### Complete countable metric space

No need'I found an example.
23. ### Complete countable metric space

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
24. ### The quotient topology

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.
25. ### The quotient topology

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
26. ### The quotient topology

Why should X have only finite number of connected components? -
27. ### The quotient topology

x~ y if and only if x and y belong to a connected set in X.S the equivalence classes ate the connected components in X
28. ### The quotient topology

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...
29. ### Argument principle for a rectangle

The image is as shown in the attached,so the change in argument is zero,am i right?
30. ### Argument principle for a rectangle

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?