# Concept derivation guides

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Concept guide



## [Topological space: fully verifying a chain of open sets on a three-point set, and recognising non-topologies](/en/derivations/derivation-mko-topological-space-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-topological-space)

Let X={a,b,c} with a, b, c distinct. (1) Prove that τ₁={∅,{a},{a,b},X} is a topology on X, covering all 16 subfamilies (including the empty one); (2) prove that τ₂={∅,{a},{b},X} is not a topology, and say which checks it does pass; (3) compare τ₁ with the indiscrete and discrete topologies; (4) on ℕ, prove that τ_fin={finite subsets of ℕ}∪{ℕ} is closed under pairwise unions and finite intersections but is not a topology.

Topological space

derivation-mko-topological-space-01





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