  The structure of topological spaces is analysed here through the lenses of
fibrous preorders. Each topological space has an associated fibrous preorder
and those fibrous preorders which return a topological space are called
spacial. A special class of spacial fibrous preorders consisting of an
interconnected family of preorders indexed by a unitary magma is called
cartesian and studied here. Topological spaces that are obtained from those
fibrous preorders, with a unitary magma \emph{I}, are called \emph{I}-cartesian
and characterized. The characterization reveals a hidden structure of such
spaces. Several other characterizations are obtained and special attention is
drawn to the case of a monoid equipped with a topology. A wide range of
examples is provided, as well as general procedures to obtain topologies from
other data types such as groups and their actions. Metric spaces and normed
spaces are considered as well.
