Abstract
In a category with a closure operator, we introduce the notion of a neighborhood of a point. The neighborhoods are then discussed and used for defining a net convergence structure on the category with respect to the closure operator. The nets considered are obtained as a categorical generalization of the usual nets. We investigate basic properties of the defined convergence. In particular, we study convergence separation and convergence compactness and describe their relationships to the usual closure separation and closure compactness.
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Mathematics Subject Classifications (2000)
18D35, 54B30, 54A05, 54A20, 54D30.
This research was supported by NATO-CNR Outreach Fellowship (No. 219.33) and by Grant Agency of the Czech Republic (No. 201/03/0933).
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Šlapal, J. F-Net Convergence with Respect to a Closure Operator. Appl Categor Struct 13, 49–64 (2005). https://doi.org/10.1007/s10485-004-3883-8
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DOI: https://doi.org/10.1007/s10485-004-3883-8