1 citations · 5 across the 10 of their papers we have counts for
Showing 2004Show all
3 papers · 1 filter
math.MG2004
The Beckman-Quarles theorem for continuous mappings from C^n to C^n
Apoloniusz Tyszka
Let varphi_n:C^n times C^n->C, varphi_n((x_1,...,x_n),(y_1,...,y_n))=sum_{i=1}^n (x_i-y_i)^2. We say that f:C^n->C^n preserves distance d>=0, if for each X,Y in C^n varphi_n(X,Y)=d…
math.MG2004★ 1 cited
The Beckman-Quarles theorem for mappings from C^2 to C^2
Apoloniusz Tyszka
Let phi: C^2 times C^2 -> C, phi((x_1,x_2),(y_1,y_2))=(x_1-y_1)^2+(x_2-y_2)^2. We say that f:C^2->C^2 preserves unit distance, if for each X,Y in C^2 phi(X,Y)=1 implies phi(f(X),f(…
math.NT2004★ 1 cited
A discrete form of the theorem that each field endomorphism of R (Q_p) is the identity
Apoloniusz Tyszka
Let K be a field and F denote the prime field in K. Let \tilde{K} denote the set of all r \in K for which there exists a finite set A(r) with {r} \subseteq A(r) \subseteq K such th…