Closure, interior and neighbourhood in a category

Authors : David HOLGATE, Josef SLAPAL

Pages : 1512-1520

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Publication Date : 2018-12-12

Article Type : Research Paper

Abstract :The natural correspondences in topology between closure, interior and neighbourhood no longer hold in an abstract categorical setting where subobject lattices are not necessarily Boolean algebras.  We analyse three canonical correspondences between closure, interior and neighbourhood operators in a category endowed with a subobject structure. While these correspondences coincide in general topology, the analysis highlights subtle differences which distinguish different approaches taken in the literature.
Keywords : Categorical closure operator, interior operator, neighbourhood operator