# Concept derivation guides

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Concept guide



## [Continuous maps between topological spaces: deciding continuity by preimages in finite spaces and separating it from openness](/en/derivations/derivation-mko-topological-continuity-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-topological-continuity)

Let X={1,2,3} with τX={∅,{1},{1,2},X}, and Y={a,b} with τY={∅,{a},Y}. For three maps given by complete tables, f (1↦a, 2↦a, 3↦b), g (1↦a, 2↦b, 3↦a) and c (everything ↦b), decide continuity by the preimage condition and decide whether each is an open map; prove that a composite of continuous maps is continuous and check it with q:Y→Z; finally count all continuous maps X→Y.

Continuous maps between topological spaces

derivation-mko-topological-continuity-01





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