Displaying similar documents to “On the ordered sets in n -dimensional real inner product spaces.”

Properties of forcing preserved by finite support iterations

Miroslav Repický (1991)

Commentationes Mathematicae Universitatis Carolinae

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We shall investigate some properties of forcing which are preserved by finite support iterations and which ensure that unbounded families in given partially ordered sets remain unbounded.

Cyclically valued rings and formal power series

Gérard Leloup (2007)

Annales mathématiques Blaise Pascal

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Rings of formal power series k [ [ C ] ] with exponents in a cyclically ordered group C were defined in []. Now, there exists a “valuation” on k [ [ C ] ] : for every σ in k [ [ C ] ] and c in C , we let v ( c , σ ) be the first element of the support of σ which is greater than or equal to c . Structures with such a valuation can be called cyclically valued rings. Others examples of cyclically valued rings are obtained by “twisting” the multiplication in k [ [ C ] ] . We prove that a cyclically valued ring is a subring of a power series...

Greedy and lazy representations in negative base systems

Tomáš Hejda, Zuzana Masáková, Edita Pelantová (2013)

Kybernetika

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We consider positional numeration systems with negative real base - β , where β > 1 , and study the extremal representations in these systems, called here the greedy and lazy representations. We give algorithms for determination of minimal and maximal ( - β ) -representation with respect to the alternate order. We also show that both extremal representations can be obtained as representations in the positive base β 2 with a non-integer alphabet. This enables us to characterize digit sequences admissible...