Computer Construction and Enumeration of All T0 and All Hyperconnected T0 Topologies on Finite Sets

Authors

A. S. Farrag, Department of Mathematics, Faculty of Science, Sohag University, Sohag, EgyptFollow
A. A. Nasef, Department of Physics and Engineering Mathematics, Faculty of Engineering, Kafrelsheikh University, Kafr El-Sheikh 33516, EgyptFollow
R. Mareay, Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafr El-Sheikh 33516, EgyptFollow

Author Country (or Countries)

Egypt

Abstract

There are many axioms on the principal topological spaces. Two of the interesting axioms are the T0 and hyperconnected topological spaces. There is a well-known and straightforward correspondence (cf. [2]) between the topologies on finite set Xn of n points and reflexive transitive relations (preorders) on those sets. This paper generalizes this result, characterizes the principal hyperconnected T0-topologies on a nonempty set X and gives their number on a set Xn. It mainly describes algorithms for construction and enumeration of all weaker and strictly weaker T0 and nT0-topologieson on Xn. The algorithms are written in fortran 77 and implemented on pentium II400 system.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/100435

Recommended Citation

S. Farrag, A.; A. Nasef, A.; and Mareay, R. (2016) "Computer Construction and Enumeration of All T0 and All Hyperconnected T0 Topologies on Finite Sets," Applied Mathematics & Information Sciences: Vol. 10: Iss. 4, Article 35.
DOI: http://dx.doi.org/10.18576/amis/100435
Available at: https://digitalcommons.aaru.edu.jo/amis/vol10/iss4/35