Abstract
We introduce and study the concept of a convergence structure for a category. Such a structure is obtained by endowing each object of the category with a convergence class subjected to some basic convergence axioms. As a tool for expressing the convergence we use categorically viewed nets which generalize the usual ones. After describing relations between convergence structures and closure operators for categories, we investigate separatedness and compactness of objects of a category with respect to a convergence structure.
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Šlapal, J. Convergence Structures for Categories. Applied Categorical Structures 9, 557–570 (2001). https://doi.org/10.1023/A:1012569528842
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DOI: https://doi.org/10.1023/A:1012569528842