Explain one statement about Stone Space In this page Stone Space This is no clear for me **"The points in S(B) are the ultrafilters on B, or equivalently the homomorphisms from B to the two-element Boolean algebra"** > I think I means every ultafilter on B is a homomorphism from B to 2 ?? I will be pleased to see some details about this.

An ultrafilter $U$ in a Boolean algebra $B$ determines a homomorphism $f:B\to2$ that sends all the elements of $U$ to 1 and all the other elements of $B$ to 0. Conversely, a homomorphism $f:B\to2$ determines the ultrafilter $f^{-1}(\\{1\\})$ in $B$. It is easy to check that these two transformations are inverse to each other.