- #1
RickilusSmith
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Homework Statement
Prove that SU(n) is closed and bounded
Homework Equations
The Attempt at a Solution
So in order to prove this, I first mapped SU(n) to be a subset of [tex]R^{{2n}^2}[/tex].
To prove the closed portion, I tried mapping a sequence in SU(n) to a sequence in [tex]R^{{2n}^2}[/tex]. However, I have trouble showing that the limit of that sequence in SU(n) is still within SU(n).
For the bounded portion, I got to the point in needing to find a radius, r, such that SU(n) is a subset of that ball of radius around the origin in [tex]R^{{2n}^2}[/tex].
However, its at these points that I'm having trouble for both problems in finding the intuition to solve them
Thanks in advance for the help!
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