= Solution
The assertion is false. Join, at one common endpoint $o$, a <line segment> of length $1/n$ for every positive <integer> $n$, and use the intrinsic <path metric>. This is a <real tree>. It is <totally bounded>, because outside the first finitely many arms every point lies arbitrarily close to $o$, and it is <complete>; hence it is <compact>. Removing $o$ leaves one <connected component> for every arm, so $o$ has countably infinite <multiplicity of a point in a real tree>.
Back to article page
