Recent content by jvt05

  1. J

    Prove intersection of convex cones is convex.

    other properties of convex cones: 1. for any positive scalar α and any x \in C, the vector αx = (α/2)x + (α/2)x is in C. 2. set C is a convex cone if and only if αC = C and C + C = C. perhaps my trouble is coming from the fact that I do not fully understand how these properties work.
  2. J

    Prove intersection of convex cones is convex.

    well set C is a convex cone if for any x,y \in C and any scalars a≥0, b≥0, ax + by \in C so let A and B be convex cones. A\bigcapB would contain all elements x \in both A and B. This is where I am having trouble.
  3. J

    Prove intersection of convex cones is convex.

    1. Let A and B be convex cones in a real vector space V. Show that A\bigcapB and A + B are also convex cones.
  4. J

    [limit point proof]: L(aub)=l(a)ul(b)

    Homework Statement Let L(X) denote the set of limit points of a set X in R^n. How do I prove that L(AUB)=L(A)UL(B)? The Attempt at a Solution I know that I have to prove that both sides are subsets of each other, but I have no clue how to start...