# Concept derivation guides

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Concept guide



## [Neighborhood: searching for open witnesses and listing all neighborhoods in a four-point topology](/en/derivations/derivation-mko-neighborhood-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-neighborhood)

Let X={1,2,3,4} and τ={∅,{1},{1,2},{3,4},{1,3,4},X}. Decide whether N1={1,2,3} and N2={2,3,4} are neighborhoods of the point 2; prove that in a finite topology the neighborhoods of x are exactly the subsets containing O_x (the intersection of all open sets containing x), and use this to list all neighborhoods of the points 1, 2, 3 and 4; prove that neighborhoods are closed upwards; and show that the verdict for the same set can change under the discrete topology.

Neighborhood

derivation-mko-neighborhood-01





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