  The tomographic histories approach is presented. As an inverse problem, we
recover in an operational way the effective topology of the extended
configuration space of a system. This means that from a series of experiments
we get a set of points corresponding to events. The difference between
effective and actual topology is drawn. We deduce the topology of the extended
configuration space of a non-relativistic system, using certain concepts from
the consistent histories approach to Quantum Mechanics, such as the notion of a
record. A few remarks about the case of a relativistic system, preparing the
ground for a forthcoming paper sequel to this, are made in the end.
