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Completeness of Inner Product Spaces and G. Cattaneo

Buhagiar D., Chetcuti E., Dvurečenskij A.

Fundamenta Informaticae

2012

Vol. 115, nr 1

15-24

In the Eighties G. Cattaneo contributed to Hilbert space quantummechanicsmodels using the family of splitting subspaces of an inner product space in order to find completeness criteria. In this paper we show how that theory was developed in the last 25 years into a rich theory which has a close connection to quantum information. G. Cattaneo also posed an open problem which was solved only this year.

Measure-theoretic characterizations of certain topological properties

Buhagiar D., Chetcuti E., Dvurečenskij A.

Bulletin of the Polish Academy of Sciences. Mathematics

2005

Vol. 53, no 1

99-109

It is shown that Cech completeness, ultracompleteness and local compactness can be denned 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.