1 citations · 5 across the 10 of their papers we have counts for
18 papers
On \emptyset-definable elements in a field
Apoloniusz Tyszka
Let K be a field and \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 that each mapping f:A(r) \to K that s…
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…
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(…
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…
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…
The Beckman-Quarles theorem for mappings from R^2 to F^2, where F is a subfield of a commutative field extending R
Apoloniusz Tyszka
Let F be a subfield of a commutative field extending R. Let ϕ_2: F^2 \times F^2 \to F, ϕ_2((x_1,x_2),(y_1,y_2))=(x_1-y_1)^2+(x_2-y_2)^2. We say that f:R^2 \to F^2 preserves distanc…