query: proof of the surjectivity of a function that satisfies certain properties
positive_passages.docid: 22061
positive_passages.text: $|f(x)-f(y)|\geq k|x-y|$.Then $f$ is bijective and its inverse is continuous.
negative_passages.docid: 146306
negative_passages.text: A continuous surjective function from $(0,1]$ onto $[0,1]$
negative_passages.docid: 16610
negative_passages.text: Surjectivity of a map from a space to itself
negative_passages.docid: 111756
negative_passages.text: How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
negative_passages.docid: 88857
negative_passages.text: Prove that Gauss map on M is surjective
negative_passages.docid: 98363
negative_passages.text: Expanding two-variable function $f(x,y)$ over the complete sets $\{ g_{i}(x) \}$ and $\{ h_{j}(y) \}$
negative_passages.docid: 104757
negative_passages.text: If $f \circ g$ is surjective, then f is surjective
negative_passages.docid: 45991
negative_passages.text: Why $f\colon \mathbb{Z}_n^\times \to \mathbb{Z}_m^\times$ is surjective?
negative_passages.docid: 28798
negative_passages.text: Proving injection and surjection with functions $F:C^B\to C^A$, $F(f)=f\circ\varphi$, $\varphi: A\to B$
negative_passages.docid: 16092
negative_passages.text: How to prove that the composition of two surjective functions is surjective
negative_passages.docid: 20437
negative_passages.text: Closed surjection that does not preserve regularity
negative_passages.docid: 58023
negative_passages.text: What is the purpose of a function being surjective?
negative_passages.docid: 64866
negative_passages.text: Proving a Composition of Functions is Bijective
negative_passages.docid: 6023
negative_passages.text: Surjectivity of Composition of Surjective Functions
negative_passages.docid: 64583
negative_passages.text: Number of surjective functions from A to B
negative_passages.docid: 130363
negative_passages.text: Prove composition of two surjections is surjection
negative_passages.docid: 97104
negative_passages.text: Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$