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Measure-Theoretic Characterizations of Certain Topological Properties

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Buhagiar D., Chetcuti E., Dvurečenskij A.
Bulletin of the Polish Academy of Sciences. Mathematics
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2005
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tom 53
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nr 1
99-109
EN
It is shown that Čech completeness, ultracompleteness and local compactness can be defined by demanding that certain equivalences hold between certain classes of Baire measures or by demanding that certain classes of Baire measures have non-empty support. This shows that these three topological properties are measurable, similarly to the classical examples of compact spaces, pseudo-compact spaces and realcompact spaces.
2
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The order topology for a von Neumann algebra

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Chetcuti E., Hamhalter J., Weber H.
Studia Mathematica
|
2015
|
tom 230
|
nr 2
95-120
EN
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.
3
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κ-compactness, extent and the Lindelöf number in LOTS

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Buhagiar D., Chetcuti E., Weber H.
Open Mathematics
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2014
|
tom 12
|
nr 8
1249-1264
EN
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.
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