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#### Ruun

##### New member

- Feb 1, 2012

- 10

\(\displaystyle G=\Big\{ \begin{pmatrix}e^{it} & 0 \\

0 & e^{iat}

\end{pmatrix} \Big| t \in \mathbb{R} \Big\}\)

0 & e^{iat}

\end{pmatrix} \Big| t \in \mathbb{R} \Big\}\)

I have to show that the closure of the set \(\displaystyle G\) is

\(\displaystyle \bar{G}=\Big\{ \begin{pmatrix}e^{it} & 0 \\

0 & e^{is}

\end{pmatrix} \Big| t \in \mathbb{R}, s \in \mathbb{R} \Big\}\)

0 & e^{is}

\end{pmatrix} \Big| t \in \mathbb{R}, s \in \mathbb{R} \Big\}\)

I don't know even how to start. I'm afraid my topolgy knowledge needs serious improvement, but I didn't think it was necessary since I picked up a Group Theory book (Lie Groups, Lie Algebras and their representations: An elementary introduction by Brian C Hall). It sad because the books looks fascinating