TY  - JOUR
TT  - On The Atoms and the Anti-Atoms of the Lattice of Topologies
AU  - Altıntaş, İsmet
PY  - 2005
DA  - June
JF  - Selcuk University Journal of  Science Faculty
JO  - sufefd
PB  - Selcuk University
WT  - DergiPark
SN  - 2458-9411
SP  - 11
EP  - 18
VL  - 1
IS  - 26
KW  - Topolojilerin latisi
KW  - atomlar
KW  - anti-atomlar
N2  - 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 antiatomic topologies, and it is observed that the number of elements of τ(X) satisfies the following expression; n(2n -2) < |τ(X)| < (2n -2) (n-1) where n = |X| (cardinality of X).
CR  - Birkhoff, G., Lattice Theory, American Mathematics Society, New York, 1967.
CR  - Grätzer, G., General Lattice Theory, Birkhäuser, Basel, 1978.
CR  - Van Rooij, A.C.M., The Lattice of All Topologies is Complemented, Can. J. Math. 20, 805-827, 1968.
CR  - Fröhlich, O., Das Halbourrdnungssystem der Topologischen Raume auf Einer Mange, Math. Ann.,156, 79-95, 1964.
CR  - Isham, C.J., Quantum Topology and Quatntisation on the Lattice of Topologies, Class Quantum Gravity 6 , 1509-1534, 198
UR  - https://dergipark.org.tr/en/pub/sufefd/article/247089
L1  - https://dergipark.org.tr/en/download/article-file/214895
ER  -