Abstract
Considering subobjects, points and a closure operator in an abstract category, we introduce a generalization of the Hausdorff separation axiom for topological spaces: the notion ofT 2-object. We discuss the properties ofT 2-objects, which depend essentially on the behaviour of points, and finally we relate them to the well-known separated objects.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
E. Čech:Topological Spaces, revised by Z. Frolík and M. Katětov, Academia, Praha, 1966.
M. M. Clementino: Separação e Compacidade em Categorias, Ph.D. Thesis, Universidade de Coimbra, 1992.
J. de Vries:Topological Transformation Groups 1, Math. Centre Tracts 65, Mathematisch Centrum, Amsterdam, 1975.
D. Dikranjan and E. Giuli: Epimorphisms and cowellpoweredness of epireflective subcategories of Top,Rend. Circ. Mat. Palermo 6 (1986), 121–136.
D. Dikranjan and E. Giuli: Closure Operators I,Topology Appl. 27 (1987), 129–143.
D. Dikranjan, E. Giuli, and W. Tholen:Closure Operators II, Categorical Topology and Its Relations to Analysis, Algebra and Combinatorics, Proc. of the Prague Int. Conf. 1988 (World Cientific, Singapore-New Jersey-London-Hong Kong), 297–335.
L. Fuchs:Infinite Abelian Groups, Vol. I, Academic Press, New York-London, 1970.
E. Giuli and M. Hušek: A diagonal theorem for epireflective subcategories of Top and cowellpoweredness,Ann. Mat. Pura Appl. 145 (1986), 337–346.
E. Giuli, S. Mantovani, and W. Tholen: Objects with closed diagonals,J. Pure Appl. Algebra 51 (1988), 129–140.
H. Herrlich, G. Salicrup, and G. E. Strecker: Factorizations, denseness, separation and relatively compact objects,Topology Appl. 27 (1987), 157–169.
I. M. James:Fibrewise Topology, Cambridge University Press, Cambridge, New York, 1989.
E. Manes: Compact Hausdorff objects,Topology Appl. 4 (1974), 341–360.
D. Pumplün and H. Röhrl: Separated totally convex spaces,Manusc. Math. 50 (1985), 145–183.
W. Tholen: Semi-topological functors I,J. Pure Appl. Algebra 15 (1979), 53–73.
S. Willard:General Topology, Addison-Wesley Publishing Company Inc., 1970.
Author information
Authors and Affiliations
Additional information
The results of this paper are essentially taken from the author's Ph. D. Thesis written under the supervision of Professors M. Sobral and W. Tholen and partially supported by a scholarship of I.N.I.C.-Instituto Nacional de Investigação Científica.