Definition Via Interior Operators
Objects: all pairs (X,int) of set X together with an interior operator int : P(X) → P(X) satisfying the following dualisation of the Kuratowski closure axioms:
- (Idempotence)
- (Preservation of binary intersections)
- (Preservation of nullary intersections)
Morphisms: all interior-preserving functions, i.e., all functions f between two interior spaces
- such that for all subsets of
Comments: The interior operator assigns to each subset its topological interior, in the same way the closure operator assigns to each subset its topological closure.
Read more about this topic: Characterizations Of The Category Of Topological Spaces
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