Ivan Shishkin, Birch Grove

Surjective map

Definition / Other /

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A surjective map is a map which has an antecedent for each element of its set of destination.

Formal definition

If f:E→Ff: E \rightarrow F, for all y∈Fy \in F, ∃x∈E\exists x \in E such as f(x)=yf(x)=y.

Practice this concept with exercises

  • 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 surjectives, montrer que hh est surjective.
    2)\textbf{2)} Supposons que hh soit surjective, montrer que gg est surjective.
    3)\textbf{3)} Supposons que hh soit surjective, est-ce que ff est nécessairement surjective ?

    Open exercise
Problems using this concept (1)
A zigzagging function?
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