query: Uniqueness of homomorphism between $\mathbb{R}_{>0}$ and $[0,1]$
positive_passages.docid: 22303
positive_passages.text: How do I prove that $f(x)f(y)=f(x+y)$ implies that $f(x)=e^{cx}$, assuming f is continuous and not zero?
negative_passages.docid: 48818
negative_passages.text: Homomorphism of local rings
negative_passages.docid: 121244
negative_passages.text: Homomorphisms and automorphisms on polynomial rings
negative_passages.docid: 148616
negative_passages.text: When is a ring homomorphism $A \to A$ surjective but not injective.
negative_passages.docid: 38257
negative_passages.text: Continuous bijection from $(0,1)$ to $[0,1]$
negative_passages.docid: 123419
negative_passages.text: Abstract algebra: homomorphism and an element of a prime order
negative_passages.docid: 27670
negative_passages.text: Group homomorphisms $\mathbb{Q}\to\mathbb{R}$
negative_passages.docid: 90192
negative_passages.text: Kernel and Image of a group homomorphism
negative_passages.docid: 14048
negative_passages.text: Proof that the complement of zero-measure set on $[0,1]$ is dense in $[0,1]$
negative_passages.docid: 82921
negative_passages.text: Uniqueness of $k$th root mod $m$ if $(k, \phi(m)) = 1$.
negative_passages.docid: 108691
negative_passages.text: Characterize the natural numbers $n$ such that there is a surjective group homomorphism from $S_n$ to $S_{n-1}$.
negative_passages.docid: 40383
negative_passages.text: Is it true that $|g| = |\phi(g)|$ for all homomorphisms $\phi: G \to G$ and $g \in G$?
negative_passages.docid: 94727
negative_passages.text: When the trace of the Frobenius homomorphism is zero?
negative_passages.docid: 84114
negative_passages.text: Does there exist a surjective homomorphism from $(\mathbb R,+)$ to $(\mathbb Q,+)$ ?
negative_passages.docid: 85242
negative_passages.text: Deciding whether two metrics are topologically equivalent in the space $C^1([0,1])$
negative_passages.docid: 120002
negative_passages.text: Prove universal morphism is unique up to unique isomorphism.
negative_passages.docid: 52012
negative_passages.text: Is there exist a homemoorphism between either pair of $(0,1),(0,1],[0,1]$