query: If there exists a surjection $f:A\to B$, can you construct an injection $f:B\to P(A)$?
positive_passages.docid: 146188
positive_passages.text: Why does a proof of $\exists f: X\to Y$ injection $\iff \exists g: Y \to X$ surjection requires the axiom of choice?
negative_passages.docid: 21707
negative_passages.text: Constructing a Bijective function via an injective and surjective one.
negative_passages.docid: 148731
negative_passages.text: Constructing a bijection between $[a,b)$ to $(0,1)$
negative_passages.docid: 121395
negative_passages.text: Let $X$ and $Y$ be non-empty sets and let $f:X \rightarrow Y$. Prove that $ f^{ −1} :P(Y ) → P(X) $ is injective if, and only if, $f$ is surjective.
negative_passages.docid: 53168
negative_passages.text: Surjective, Injective, Bijective Functions from $\mathbb Z$ to itself
negative_passages.docid: 148500
negative_passages.text: Understanding this theorem and how to go about proving it surjectivity?
negative_passages.docid: 63146
negative_passages.text: Proof of properties of injective and surjective functions.
negative_passages.docid: 84114
negative_passages.text: Does there exist a surjective homomorphism from $(\mathbb R,+)$ to $(\mathbb Q,+)$ ?
negative_passages.docid: 19245
negative_passages.text: Schwartz Distribution Theory: (Non-)Surjectivity of $f \mapsto f*f$ in $ \mathcal E '$
negative_passages.docid: 51334
negative_passages.text: Does there exist any surjective group homomorphism from $(\mathbb R^* , .)$ onto $(\mathbb Q^* , .)$?
negative_passages.docid: 136842
negative_passages.text: $|x-f(x)|<5777$, Show that $f$ is surjective
negative_passages.docid: 16610
negative_passages.text: Surjectivity of a map from a space to itself
negative_passages.docid: 138481
negative_passages.text: $f(x)=x/1$ is not injective?
negative_passages.docid: 45380
negative_passages.text: Surjectivity implies injectivity and conversely
negative_passages.docid: 148569
negative_passages.text: Embeddings $A → B → A$, but $A \not\cong B$?
negative_passages.docid: 50649
negative_passages.text: On the existence of a continuous bijection $f\colon [0,1]\to [0,1]\times [0,1]$
negative_passages.docid: 93776
negative_passages.text: Bijective mapping between $\mathbb{R}^2$ and $\mathbb{R}$?