1. L

    Symmetry between all null and all unbounded sets

    Is there a greatest symmetry between the set of all null sets and the set of all unbounded sets?
  2. G

    An example of a compact multiplicatively unbounded ring

    My teacher asked me to build an associative topological Hausdorff compact ring R with 1, which is multiplicatively unbounded. That means there is a neighborhood U∋1 such that FU≠R for each finite subset F of R. I am somewhat stuck, because I have a small stock of topological rings, and I...
  3. J

    measure of unbounded set

    Suppose A is not a bounded set and m(A?B)?(3/4)m(B) for every B. what is m(A)?? here, m is Lebesgue Outer Measure My attemption is : Let An=A?[-n,n], then m(A)=lim m(An)= lim m(An?[-n,n]) ? lim (3/4)m([-n,n]) = infinite. is my solution right? I am confusing m(A) < infinite , it doest make...
  4. A

    Minimum Real Part theorem issue on RHP (unbounded domain)

    Hello to everybody.. this is my first login... I need some help with the minimum real part theorem ( similar to the max-min modulus theorem) of a complex function analytic in a (bounded) D domain... The proof of the theorem in the case of a limited (bounded) domain is similar to that of max...
  5. A

    Unbounded function on a closed graph

    A graph is defined as G := {(x,f(x)), x in A (a subset of Rn) and f(x) in R}. I am trying to find a function that is unbounded, while the graph G is closed to show that A (a subset of Rn) is not necessarily closed. I am also having difficulty in seeing how G can be closed if A is not necessarily...
  6. B

    Complex Unbounded Sets

    Is a bounded set synonymous to a set that goes to infinity? I feel like unless a set is (-infinity, n) or [n, infinity) it is not going to be unbounded. The other thing that I was wondering is can a set be "neither open nor closed" AND unbounded? Doesn't the definition of open/closed imply that...
  7. R

    unbounded sequence

    let x_n be an unbounded sequence . prove that there is a subsequence x_{n_k} of x_n such that \frac{1}{x_{n_k}} \to 0