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. ) 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)
S. Farrag, A.; A. Nasef, A.; and Mareay, R.
"Computer Construction and Enumeration of All T0 and All Hyperconnected T0 Topologies on Finite Sets,"
Applied Mathematics & Information Sciences: Vol. 10
, Article 35.
Available at: https://dc.naturalspublishing.com/amis/vol10/iss4/35