Topogenous Structures on Categories
Minani Iragi · University of the Western Cape Electronic Theses and Dissertations Repository (University of the Western Cape) · 2016
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.November 2016.It is important to observe from the above two propositions that -closed and -initial morphisms behave in a similar way as their conterpart in neighbourhood notations.We next provide an immediate connection between the notions of -initiality and -closedness.