Dear Colleagues,

Could you please help me in solving the following problem:

Show that the subspace consisting of all such that is complete.

Best Regards.

Printable View

- April 7th 2011, 04:28 AMraedA complete Metric Space
Dear Colleagues,

Could you please help me in solving the following problem:

Show that the subspace consisting of all such that is complete.

Best Regards. - April 7th 2011, 05:29 AMOpalg
- April 7th 2011, 06:03 AMraed
Okay I understand that but how can I prove that x(a)=x(b) ?

- April 7th 2011, 06:29 AMOpalg
- April 7th 2011, 12:43 PMDrexel28
Perhaps simpler than pure definition (though not much) is to notice that the linear functional is continuous and thus (our set) is a closed subspace of the complete space and thus complete (this is easier assuming that you know (which I've stated to you before and which is a very simple fact) that the evaluation functionals is continuous and thus continuous).