\(F\)-net convergence with respect to a closure operator (Q1781090)

The author gives the notion of neighborhood in a category with a closure operator, and then, applies the theory of convergence structures in a general category developed by himself [\textit{J. Šlapal}, ``Convergence structures for categories'', Appl. Categ. Struct. 9, 557--570 (2001; Zbl 1006.18005)] to investigate the net convergence structure on a category with respect to a closure operator. Basic properties of this kind of net convergence structures were studied, including their relationship to notions of separation and compactness.