Valuations of lines
نویسنده
چکیده
We enlarge the problem of valuations of triads on so called lines. A line in an e-structure A = 〈A, F,E〉 (it means that 〈A, F 〉 is a semigroup and E is an automorphism or an antiautomorphism on 〈A,F 〉 such that E ◦ E = Id ↾ A) is, generally, a sequence A ↾ B, A ↾ Uc, c ∈ FZ (where FZ is the class of finite integers) of substructures of A such that B ⊆ Uc ⊆ Ud holds for each c ≤ d. We denote this line as A(Uc, B)c∈FZ and we say that a mapping H is a valuation of the line A(Uc, B)c∈FZ in a line Â(Ûc, B̂)c∈FZ if it is, for each c ∈ FZ, a valuation of the triad A(Uc, B) in Â(Ûc, B̂). Some theorems on an existence of a valuation of a given line in another one are presented and some examples concerning equivalences and ideals are discussed. A generalization of the metrization theorem is presented, too.
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