Displaying similar documents to “Monotonic valuations of π σ -triads and evaluations of ideals”

Valuations of lines

Josef Mlček (1992)

Commentationes Mathematicae Universitatis Carolinae

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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 U c , c 𝐅𝐙 (where 𝐅𝐙 is the class of finite integers) of substructures of 𝔸 such that B U c U d holds for each c d . We denote this line as 𝔸 ( U c , B ) c 𝐅𝐙 and we say that a mapping H is a valuation of the line 𝔸 ( U c , B ) c 𝐅𝐙 in a line 𝔸 ^ ( U ^ c , B ^ ) c 𝐅𝐙 if it is, for each c 𝐅𝐙 , a valuation of the triad 𝔸 ( U c , B ) in 𝔸 ^ ( U ^ c , B ^ ) . Some theorems on an...

Indiscernibles and dimensional compactness

C. Ward Henson, Pavol Zlatoš (1996)

Commentationes Mathematicae Universitatis Carolinae

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This is a contribution to the theory of topological vector spaces within the framework of the alternative set theory. Using indiscernibles we will show that every infinite set u S G in a biequivalence vector space W , M , G , such that x - y M for distinct x , y u , contains an infinite independent subset. Consequently, a class X G is dimensionally compact iff the π -equivalence M is compact on X . This solves a problem from the paper [NPZ 1992] by J. Náter, P. Pulmann and the second author.