  In this essay, a general case of information systems contains 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, as an applied example, a mathematical model for
knowledge spread is introduced.
