Abstract
Bu çalışmada, bir sonlu X kümesi üzerine kurulan bütün topolojilerin τ(X) ailesinin latisindeki atomların bazı özellikleri ispat edildi. Ayrıca, topolojilerin atom ve anti-atom sayılarını bullmak için bir geometric yöntem verildi ve τ(X) ailesinin elemanlarının sayısı, |τ(X)| için n(2n -2) < |τ(X)| < (2n -2) (n-1) ifadesinin sağlandığı gözlemlendi.
Keywords
References
- Birkhoff, G., Lattice Theory, American Mathematics Society, New York, 1967.
- Grätzer, G., General Lattice Theory, Birkhäuser, Basel, 1978.
- Van Rooij, A.C.M., The Lattice of All Topologies is Complemented, Can. J. Math. 20, 805-827, 1968.
- Fröhlich, O., Das Halbourrdnungssystem der Topologischen Raume auf Einer Mange, Math. Ann.,156, 79-95, 1964.
- Isham, C.J., Quantum Topology and Quatntisation on the Lattice of Topologies, Class Quantum Gravity 6 , 1509-1534, 198
Abstract
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).
Keywords
References
- Birkhoff, G., Lattice Theory, American Mathematics Society, New York, 1967.
- Grätzer, G., General Lattice Theory, Birkhäuser, Basel, 1978.
- Van Rooij, A.C.M., The Lattice of All Topologies is Complemented, Can. J. Math. 20, 805-827, 1968.
- Fröhlich, O., Das Halbourrdnungssystem der Topologischen Raume auf Einer Mange, Math. Ann.,156, 79-95, 1964.
- Isham, C.J., Quantum Topology and Quatntisation on the Lattice of Topologies, Class Quantum Gravity 6 , 1509-1534, 198
Details
| Other ID | JA58JV36ZJ |
|---|---|
| Authors | |
| Submission Date | June 1, 2005 |
| Publication Date | June 1, 2005 |
| IZ | https://izlik.org/JA59EB37WZ |
| Published in Issue | Year 2005 Volume: 1 Issue: 26 |
Cite
Journal Owner: On behalf of Selçuk University Faculty of Science, Rector Prof. Dr. Hüseyin YILMAZ
Selcuk University Journal of Science Faculty accepts articles in Turkish and English with original results in basic sciences and other applied sciences. The journal may also include compilations containing current innovations.
It was first published in 1981 as "S.Ü. Fen-Edebiyat Fakültesi Dergisi" and was published under this name until 1984 (Number 1-4).
In 1984, its name was changed to "S.Ü. Fen-Edeb. Fak. Fen Dergisi" and it was published under this name as of the 5th issue.
When the Faculty of Letters and Sciences was separated into the Faculty of Science and the Faculty of Letters with the decision of the Council of Ministers numbered 2008/4344 published in the Official Gazette dated 3 December 2008 and numbered 27073, it has been published as "Selcuk University Journal of Science Faculty" between 2009-2025.
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