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Abstrakty
On a non-trivial partially ordered real vector space (V,≤) the orthogonality relation is defined by incomparability and ζ(V,⊥) is a complete lattice of double orthoclosed sets. We say that A ⊆ V is an orthogonal set when for all a,b ∈ A with a ≠ b, we have a ⊥ b. In our earlier papers we defined an integrally open ordered vector space and two closure operations A → D(A) and $A → A^{⊥⊥}$. It was proved that V is integrally open iff $D(A) = A^{⊥⊥}$ for every orthogonal set A ⊆ V. In this paper we generalize this result. We prove that V is integrally open iff D(A) = W for every W ∈ ζ(V,⊥) and every maximal orthogonal set A ⊆ W. Hence it follows that the lattice ζ(V,⊥) is orthomodular.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
129-133
Opis fizyczny
Daty
wydano
2010
Twórcy
autor
- Institute of Mathematics, University of Economics, Komandorska 118/120, 53-345 Wrocław, Poland
Bibliografia
Typ dokumentu
Bibliografia
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DOI
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-bc89-0-7