On The Atoms and the Anti-Atoms of the Lattice of Topologies

İsmet Altintaş
2005 Fak Fen Derg Sayı   unpublished
In this paper, some properties of the atoms in the lattice of a family τ(X) of all topologies on a finite set X are proved. In addition, a geometric method is given to find the number of the atomic and the anti-atomic topologies, and it is observed that the number of elements of τ(X) satisfies the following expression; n(2 n-2) < |τ(X)| < (2 n-2) (n-1) where n = |X| (cardinality of X).