Applied Categorical Structures

, Volume 27, Issue 6, pp 703–721 | Cite as

Neighbourhood Operators: Additivity, Idempotency and Convergence

  • A. RazafindrakotoEmail author


We define and discuss the notions of additivity and idempotency for neighbourhood and interior operators. We then propose an order-theoretic description of the notion of convergence that was introduced by D. Holgate and J. Šlapal with the help of these two properties. This will provide a rather convenient setting in which compactness and completeness can be studied via neighbourhood operators. We prove, among other things, a Frolík-type theorem with the introduction of reflecting morphisms.


Neighbourhood operators Interior operators Idempotency Additivity Kleisli composition Kan extension Compactness Convergence Filters 

Mathematics Subject Classification

18B30 54B30 54C10 18B35 


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Authors and Affiliations

  1. 1.Department of Mathematics and Applied MathematicsUniversity of the Western CapeBellvilleSouth Africa

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