[ Nombre de topologies finies sur un ensemble fini: Une approche de décomposition en topologies partielles ]
Volume 67, Issue 2, July 2023, Pages 249–258
Clara Paluku Kasoki1 and Salem Kumpovela2
1 Departement de Mathématique et Informatique, Faculté des Sciences, Université pédagogique nationale, Kinshasa, RD Congo
2 Departement de Mathématique et Informatique, Faculté des Sciences, Université pédagogique nationale, Kinshasa, RD Congo
Original language: French
Copyright © 2023 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This article deals with finite topological spaces. It shows that the set of all finite topologies on a finite set with n elements is the union of sets of partial topologies on X, where the number of elements in each set varies between 2 and 2n. The number of partial topologies with k elements on X is also determined, as well as the number of finite topologies on X using these results.
Author Keywords: Finite topological space, partial topology, cardinality, finite set.
Volume 67, Issue 2, July 2023, Pages 249–258
Clara Paluku Kasoki1 and Salem Kumpovela2
1 Departement de Mathématique et Informatique, Faculté des Sciences, Université pédagogique nationale, Kinshasa, RD Congo
2 Departement de Mathématique et Informatique, Faculté des Sciences, Université pédagogique nationale, Kinshasa, RD Congo
Original language: French
Copyright © 2023 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
This article deals with finite topological spaces. It shows that the set of all finite topologies on a finite set with n elements is the union of sets of partial topologies on X, where the number of elements in each set varies between 2 and 2n. The number of partial topologies with k elements on X is also determined, as well as the number of finite topologies on X using these results.
Author Keywords: Finite topological space, partial topology, cardinality, finite set.
Abstract: (french)
Cet article traite des espaces topologiques finis. Il montre que l’ensemble de toutes les topologies finies sur un ensemble fini à n éléments est la réunion d’ensembles de topologies partielles sur X, où le nombre d’éléments dans chaque ensemble varie entre 2 et 2n. Le nombre de topologies partielles à k éléments sur X est également déterminé, ainsi que le nombre de topologies finies sur en utilisant ces résultats.
Author Keywords: Espace topologique fini, topologie partielle, cardinalité, ensemble fini.
How to Cite this Article
Clara Paluku Kasoki and Salem Kumpovela, “Number of finite topologies on a finite set: An approach of decomposition into partial topologies,” International Journal of Innovation and Scientific Research, vol. 67, no. 2, pp. 249–258, July 2023.
