Ivan Shishkin, Birch Grove

Injective map

Definition / Other /

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An injective map is a map which has at least one unique preimage for each element of its set of destination.

Formal definition

For two sets AA and BB, the map f:A→Bf: A \rightarrow B is injective if and only if, we have:
∀y∈B\forall y \in B, there is at least one x∈Ax \in A such as f(x)=yf(x)=y.

Practice this concept with exercises

1 / 3

  • Soient EE, FF et GG des ensembles.
    Soient f:E→Ff : E \to F, g:F→Gg : F \to G et h=g∘fh = g \circ f des applications.
    \newline
    1)\textbf{1)} Supposons que ff et gg soient injectives, montrer que hh est injective.
    2)\textbf{2)} Supposons que hh soit injective, montrer que ff est injective.
    3)\textbf{3)} Supposons que hh soit injective, est-ce que gg est nécessairement injective ?

    Open exercise
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