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In this paper, a general case of information systems containing quantum information systems is considered. By presenting an algorithmic method, a new kind of information topology is defined and considered. Continuous maps between two information topological spaces are studied. Moreover, open and compact information systems are taken into consideration. It is also proved that a finite product of compact information systems is a compact information system. Following that, two methods for constructing new open covers for a class of compact information systems are presented, and information topological entropy for continuous self-maps of an information topological space is considered. We show that information topological entropy is an invariant object under a conjugate relation. Finally, a mathematical model for knowledge spread is introduced.

The effect of an information system on the learning of the space structure