Main Article Content
Compactness with respect to a convergence structure
Abstract
A convergence structure for a category is given by
determining convergent nets and their limits for each object of this category
under validity of some basic convergence axioms. The nets considered are
obtained as a categorical generalization of the usual nets. A convergence
structure for a category induces, under some natural conditions, a closure
operator of this category. We study separatedness and
compactness of objects of a given category with respect to a convergence
structure and show that they behave more naturally than the usual separatedness and compactness of topological spaces.
Mathematics Subject Classification
(2000): 18D35, 54B30, 54A20, 54D30.
Key words: Convergence structure for a
category; limit object; separated object; compact object.
Quaestiones
Mathematicae 25 (2002), 19-27
determining convergent nets and their limits for each object of this category
under validity of some basic convergence axioms. The nets considered are
obtained as a categorical generalization of the usual nets. A convergence
structure for a category induces, under some natural conditions, a closure
operator of this category. We study separatedness and
compactness of objects of a given category with respect to a convergence
structure and show that they behave more naturally than the usual separatedness and compactness of topological spaces.
Mathematics Subject Classification
(2000): 18D35, 54B30, 54A20, 54D30.
Key words: Convergence structure for a
category; limit object; separated object; compact object.
Quaestiones
Mathematicae 25 (2002), 19-27
