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  1. H

    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
  2. H

    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.
  3. H

    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)
  4. H

    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
  5. H

    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?
  6. H

    Determinant of a unit columns matrix

    Yes,i know that but i am searching for a proof.
  7. H

    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
  8. H

    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.
  9. H

    Matrix logarithm

    And how do i do that?
  10. H

    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...
  11. H

    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
  12. H

    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...
  13. H

    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.
  14. H

    Imbedding of the ratiomals

    But Cauchy sequence in Q may not be Cauchy in the complete space.Homeomorphism preserves the topology,not the metric.
  15. H

    Imbedding of the ratiomals

    why,beacause the imbedded image must be closed hence topologically complete?Why does it have to be closed?
  16. H

    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?
  17. H

    Product space

    Is there atopological space X such that XxX (the product space) is homeomorphic to the unit circle in the plane
  18. H

    Locally path connected

    hahn mazurkiewicz theorem gives the answer
  19. H

    Locally path connected

    You mean to show that this is clopen?This is my difficulty.I suppose the compacity is needed
  20. H

    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.
  21. H

    Complete countable metric space

    No need'I found an example.
  22. H

    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
  23. H

    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.
  24. H

    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
  25. H

    The quotient topology

    Why should X have only finite number of connected components? -
  26. H

    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
  27. H

    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...
  28. H

    Argument principle for a rectangle

    The image is as shown in the attached,so the change in argument is zero,am i right?
  29. H

    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?
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