Our simple experimental application Random Topology Generator uses the Wolfram Mathematica internal generator of pseudo-random numbers for simulation of random choice of a topology on a given finite set. The implemented algorithm ensures that all choices of each particular topology have (approximately) the same probability. The motivation is inspired by the joint paper  of the first author. The perceived topology of the universe may be a result of certain physical processes on a particle level, which probably have a random character. The purpose of the application is a simulation of this random process of topology generation and for testing the conjecture whether the locally Euclidean, manifold topology that is perceived at the large scale level, is, in some sense, a statistical average of these randomly generated and dynamically changing topologies arising on the particle level.
The given underlying set X:.
The number of points of X:
The number of all topologies on X:
The probability of the choice of a single particular topology:
A randomly generated topology τ on X:
The application Random Topology Generator is written in Java powered by Wolfram webMathematica 3.1. The application is hosted at the server of the Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology. For research and scientific activities the software is available free of charge. In all other cases, please contact RNDr. M. Novák, Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická 8, 616 00 Brno, phone: +420 5 4114 3135. Acknowledgement: FEKT-S-11-2/921 "Vlastnosti řešení funkcionálních diferenciálních a diferenčních rovnic"