Computer construction and enumeration of all topologies and all hyperconnected topologies on finite sets

Abstract

In [1] the present authors described an algorithm to construct and enumerate specific topologies on a finite set X _n of n points that is the strictly weaker topologies on X _n than a given topology each of which is not contained in any excluding point topology on X _n . In this paper we describe an algorithm to construct and enumerate all topologies and all hyperconnected topologies on X _n . The topologies on X _n which are weaker than a given topology on X _n will be constructed and enumerated. The algorithm is written in Fortran 77 and implemented on an Pentium 400 system.

Keywords:

• Topology space
• hyperconnected topologies
• finite sets

C. R. Category::

• Topology space
• F.2.1