  It is well known that the description of topological and geometric properties
of bisectors in normed spaces is a non-trivial subject. In this paper we
introduce the concept of bounded representation of bisectors in finite
dimensional real Banach spaces. This useful notion combines the concepts of
bisector and shadow boundary of the unit ball, both corresponding with the same
spatial direction. The bounded representation visualizes the connection between
the topology of bisectors and shadow boundaries (Lemma 1) and gives the
possibility to simplify and to extend some known results on radial projections
of bisectors. Our main result (Theorem 1) says that in the manifold case the
topology of the closed bisector and the topology of its bounded representation
are the same; they are closed, $(n-1)$-dimensional balls embedded in Euclidean
$n$-space in the standard way.
