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We introduce and study a concept of neighborhoods with respect to a categorical closure operator. The concept, which is based on using pseudocomplements in subobject lattices, naturally generalizes the classical neighborhoods in topological spaces and we show that it behaves accordingly. We investigate also separation and compactness defined in a natural way by the help of the neighboorhoods introduced.

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Acta Mathematica Hungarica
G. C. L. Brümmer
E. Giuli
, and
D. Holgate
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