Let (X,c) be a Čech closure
space. By M we denote the family of all proximities of Čech on X which induce c.
M is known to be a complete lattice under set inclusion as ordering. The
analogue of the R0 separation axiom as defined for topological spaces is
introduced into closure spaces. R0-closure spaces are exactly those spaces for
which M≠ϕ. Other characterizations for R0-closure spaces are presented. The
most interesting one is: every R0-closure space is a subspace of a product
of a certain number of copies of a fixed R0− closure space. A number of
techniques for constructing elements of M are developed. By means of one of
these constructions, all covers of any member of M can be obtained. Using
these constructions the following structural properties of M are derived: M
is strongly atomic, M is distributive, M has no antiatoms, |M| = 0,1 or
|M|≧ 22ℵ0.
