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The order topology for a von Neumann algebra

Emmanuel Chetcuti, Jan Hamhalter, Hans Weber (2015)

Studia Mathematica

The order topology τ o ( P ) (resp. the sequential order topology τ o s ( P ) ) on a poset P is the topology that has as its closed sets those that contain the order limits of all their order convergent nets (resp. sequences). For a von Neumann algebra M we consider the following three posets: the self-adjoint part M s a , the self-adjoint part of the unit ball M ¹ s a , and the projection lattice P(M). We study the order topology (and the corresponding sequential variant) on these posets, compare the order topology to the other...

The ordering of commutative terms

Jaroslav Ježek (2006)

Czechoslovak Mathematical Journal

By a commutative term we mean an element of the free commutative groupoid F of infinite rank. For two commutative terms a , b write a ≤ b if b contains a subterm that is a substitution instance of a . With respect to this relation, F is a quasiordered set which becomes an ordered set after the appropriate factorization. We study definability in this ordered set. Among other things, we prove that every commutative term (or its block in the factor) is a definable element. Consequently, the ordered set has...

The prime and maximal spectra and the reticulation of BL-algebras

Laurenťiu Leuštean (2003)

Open Mathematics

In this paper we study the prime and maximal spectra of a BL-algebra, proving that the prime spectrum is a compact T 0 topological space and that the maximal spectrum is a compact Hausdorff topological space. We also define and study the reticulation of a BL-algebra.

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