The Listing of Topologies Close to the Discrete One on Finite Sets

被引：3
|
作者：
Velichko, I. G. [1 ]
Stegantseva, P. G. [2 ]
Bashova, N. P. [2 ]
机构：
[1] Tavria State Agrotechnol Univ, Pr B Khmelnitskogo 18, UA-72310 Melitopol, Zaporozhye Regi, Ukraine
[2] Zaporozhye Natl Univ, UA-69600 Zaporozhe, Ukraine
来源：
RUSSIAN MATHEMATICS | 2015年 / 59卷 / 11期
关键词：
topology on a finite set; T-0-topology; index of an element of a topology; index of a topology; vector of a topology;
D O I：
10.3103/S1066369X1511002X
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider T-0-topologies on n-element set that contain more than 2(n) elements. We solve a problem of listing and counting of such topologies. For this purpose we introduce the notions of an index of the topology and a vector of the topology. We study their properties and single out all possible classes of the topologies under the consideration. We formulate and prove a theorem related to the number of the topologies in each of the classes.
引用
收藏
页码：19 / 25
页数：7
相关论文
共 50 条
12345