  Theoretically speaking, there are four kinds of possibilities to define the
random conjugate space of a random locally convex module. The purpose of this
paper is to prove that among the four kinds there are only two which are
universally suitable for the current development of the theory of random
conjugate spaces: in this process we also obtain a somewhat surprising and
crucial result that for a random normed module with base $(\Omega,{\cal F},P)$
such that $(\Omega,{\cal F},P)$ is nonatomic then the random normed module is a
totally disconnected topological space when it is endowed with the locally
$L^{0}-$convex topology.
