# Concept derivation guides

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Concept guide



## [Open and closed sets: classifying all sixteen subsets of a four-point topology](/en/derivations/derivation-mko-open-closed-set-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-open-closed-set)

Let X={1,2,3,4} and τ={∅,{1},{1,2},{3,4},{1,3,4},X}. First verify that τ is a topology on X, then list all closed sets and sort the sixteen subsets of X into four classes: clopen, open only, closed only, and neither; finally prove that in every topological space ∅ and X are clopen, and that the union of two closed sets is closed.

Open and closed sets

derivation-mko-open-closed-set-01





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