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

TL;DR

This paper introduces a new framework for information topology within quantum information systems, exploring properties like compactness and entropy, and applies it to model knowledge dissemination.

Contribution

It defines a novel information topology, studies continuous maps and entropy in this context, and presents a mathematical model for knowledge spread.

Findings

Finite products of compact information systems are compact.

Information topological entropy is invariant under conjugation.

A mathematical model for knowledge spread is developed.

Abstract

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.