Soit-f-E-F-une-application-P-E-est-l-ensemble-des-parties-de-E-Montrer-que-f-est-surjective-B-P-E-f-f-1-B-B-

Tinku Tara June 4, 2023 None 0 Comments

Question Number 161205 by mathocean1 last updated on 14/Dec/21

Soit f: E→F une application. P(E) est l′ensemble des parties de E. Montrer que: f est surjective⇔∀ B ∈ P(E), f(f^(−1) (B))=B.

$${Soit}\:{f}:\:{E}\rightarrow{F}\:{une}\:{application}.\: \\ $$$$\mathscr{P}\left({E}\right)\:{est}\:{l}'{ensemble}\:{des}\:{parties} \\ $$$${de}\:{E}.\:{Montrer}\:{que}: \\ $$$${f}\:{est}\:{surjective}\Leftrightarrow\forall\:{B}\:\in\:\mathscr{P}\left({E}\right),\:{f}\left({f}^{−\mathrm{1}} \left({B}\right)\right)={B}. \\ $$

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Soit-f-E-F-une-application-P-E-est-l-ensemble-des-parties-de-E-Montrer-que-f-est-surjective-B-P-E-f-f-1-B-B-

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