Topogenous Structures on Categories

• Main Author: Iragi, Minani
• Other Authors: Holgate, David B.
• Language: en
• Published: University of the Western Cape 2019
• Subjects: Topogenous orders; Categorical neighbourhood operators; Proximity and uniform structures; Syntopogenous structures
• Online Access: http://hdl.handle.net/11394/6717

>Magister Scientiae - MSc === Although the interior operators correspond to a special class of neighbourhood operators, the closure operators are not nicely related to the latter. We introduce and study the notion of topogenous orders on a category which provides a basis for categorical study of topology. We show that they are equivalent to the categorical neighbourhood operators and house the closure and interior operators. The natural notion of strict morphism with respect to a topogenous order is shown to capture the known ones in the settings of closure, interior and neighbourhood operators.