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The order topology for a von Neumann algebra

100%

Chetcuti E. , Hamhalter J. , Weber H.

Studia Mathematica

2015

tom 230

nr 2

95-120

The order topology $τ_{o}(P)$ (resp. the sequential order topology $τ_{os}(P)$) 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 $M_{sa}$, the self-adjoint part of the unit ball $M¹_{sa}$, 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 standard locally convex topologies on M, and relate the properties of the order topology to the underlying operator-algebraic structure of M.

κ-compactness, extent and the Lindelöf number in LOTS

100%

Buhagiar D. , Chetcuti E. , Weber H.

nr 8

1249-1264

We study the behaviour of ℵ-compactness, extent and Lindelöf number in lexicographic products of linearly ordered spaces. It is seen, in particular, that for the case that all spaces are bounded all these properties behave very well when taking lexicographic products. We also give characterizations of these notions for generalized ordered spaces.