7
$\begingroup$

How can I show that, if a Frechet space is not normable then, there is no countable base of bounded sets.

A collection $\Gamma$ of subsets of X is called a base for bounded sets, if for any bounded set C there is a $B_{0}$ such that C is contained in $B_{0}$

Mahmut çükübikyan

  • 0
    Do you assume that elements of base are open sets?2012-05-14
  • 0
    No just sets in $X$.2012-05-14
  • 0
    In the definition of "base of bounded sets" sets themselves should also be bounded. So "base of bounded sets" means that A collection Γ of bounded subsets of X is called a base for bounded sets, if for any bounded set C there is a B0 such that C is contained in B02012-05-14
  • 0
    Of course why should we call as a base of bouded sets?2012-05-16

1 Answers 1