C. A. Petri, the initiator of the theory of Petri nets, proposes a new approach in this area. This approach offers a topological view of the net theory, outlining the continuous aspects of this theory, and considers the role of continuity and uncertainty in the context of measurement and control, and safety and security problems. A construction of a metric space is proposed.

Petri points out the close relations between the modeling approach proposed here and different models occurring in topology, physics (the Lorentz transformation), and logic. He also discusses new bridges from space-time geometry to computation.

The paper opens a new approach to the Petri net theory and settles unexpected links between this theory and other research fields. After approximately 35 years of development in the fruitful research area of Petri net theory, its originator proposes a new vision of the field.