Applied Mathematics & Information Sciences

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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.

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