Net spaces in categorical topology

被引：12
作者：
Slapal, J
机构：
[1] Department of Mathematics, Technical University of Brno, 616 69 Brno
来源：
PAPERS ON GENERAL TOPOLOGY AND APPLICATIONS: ELEVENTH SUMMER CONFERENCE AT THE UNIVERSITY OF SOUTHERN MAINE | 1996年 / 806卷
关键词：
S-net; subnet; S-net space; convergence S-net space; limit S-net space; topological category; Cartesian closed category; topological universe; diagonality axiom; condition of iterated limits; preclosure space; closure space; pseudo-topological space; topological space; R(1)-space; T-0-space; T-1-space;
D O I：
10.1111/j.1749-6632.1996.tb49183.x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In the paper we introduce the notion of S-nets, S a nonempty construct, as a generalization of the usual nets. S-net spaces and continuous maps between them are then defined in a natural way. For S-net spaces we introduce a number of axioms and study the categories obtained. We find some topological and Cartesian closed categories of S-net spaces and describe their relations to certain known topological categories.
引用
收藏
页码：393 / 412
页数：20
相关论文
共 15 条
[1]  
Adamek J., 1990, ABSTRACT CONCRETE CA
[2]  
Cech E., 1966, TOPOLOGICAL SPACES
[3]  
Cech E., 1968, Topological Papers of Eduard Cech, P436
[4]  
Dudley RM., 1964, Trans. Am. Soc, V112, P483, DOI [DOI 10.1090/S0002-9947-1964-0175081-6, 10.1090/S0002-9947-1964-0175081-6]
[5]  
EDGAR GA, 1976, GEN TOPOL APPL, V6, P65
[6]  
Engelking R., 1977, Math. Monographs, V60
[7]  
KELLEY JL, 1963, GENERAL TOPOLOGY
[8]  
Koutsky K., 1960, PUBL FS U BRNO, V410, P45
[9]  
Kuratowski K., 1966, Topology, V1
[10]  
Novak J, 1964, CHECHOSLOVAK MATH J, V14, P548
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