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Taking the Cambridge part III 2012-2013.


Sep
24
awarded  Autobiographer
Jul
18
awarded  Yearling
Apr
23
comment Is $L^\infty(\mu)$ a locally compact Hausdorff space?
I hope the edit is helpful?
Apr
23
revised Is $L^\infty(\mu)$ a locally compact Hausdorff space?
more detail
Apr
22
comment Is $L^\infty(\mu)$ a locally compact Hausdorff space?
Any introductory Functional Analysis textbook I guess? Try Linear Analysis by Bollobas
Apr
22
answered Does sequential limits coincide with topology limits?
Apr
22
answered Is $L^\infty(\mu)$ a locally compact Hausdorff space?
Apr
22
comment Expectation of Random Variables - Measure Theory
Use dominated convergence.
Apr
19
comment A finely open set, not open up to polar set?
Oops, sorry about that
Apr
19
comment A finely open set, not open up to polar set?
I'm not familiar with finitely open sets, but they seem similar to radially/algebraically open sets. A nice example of such a set that is very far from being open is to take the complement of a dense subset of the plane that has no three points colinear.
Mar
25
accepted Are projections onto closed complemented subspaces of a topological vector space always continuous?
Mar
25
awarded  Commentator
Mar
25
comment Are projections onto closed complemented subspaces of a topological vector space always continuous?
Thanks for the counterexample; I had my hopes up that it would be true in general. The test function topology is complete (if that's the right word for Cauchy sequences converging in a topological vector space) which may rule out this kind of behaviour
Mar
24
answered Stone-Čech compactification of completely regular space
Mar
24
awarded  Student
Mar
24
asked Are projections onto closed complemented subspaces of a topological vector space always continuous?
Jul
27
comment Do such sequences exist?
Oops! You're right.
Jul
27
answered Do such sequences exist?
Jul
27
comment Do such sequences exist?
I've got a proof that doesn't use any linear algebraic arguments, I guess I'll post it
Jul
27
comment Do such sequences exist?
I think I've thought of how to do it