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\begin{document}
\pro : Let $X\subset \Bbb R$ be the set of points $1, \frac{1}{2}, \frac{ 1}{3},...$ and $0$. For the C*-algebra $M_2$ of
two-by-two matrices denote by $C(X;M_2)$ the set of all continuous functions on
$X$ with values in $ M_2$. Put $B_1 =\{f \in C(X;M_2) :~ f(0)$~{ is diagonalg}$\}$, $B_2 = \{f \in
C(X;M_2) :~ f(0) ${ has the form 
\begin{eqnarray*}
\mathbf (X) = \left(
\begin{array}{cc}
*&0\\
0&0
\end{array}\right)
\end{eqnarray*}

 $\}$.
\end{document}