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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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