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Computer Construction and Enumeration of All T0 and All Hyperconnected T0 Topologies on Finite Sets |
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PP: 1565-1570 |
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doi:10.18576/amis/100435
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Author(s) |
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A. S. Farrag,
A. A. Nasef,
R. Mareay,
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Abstract |
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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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