Displaying similar documents to “Sequential convergences on Boolean algebras defined by systems of maximal filters”

Sequential closedness of Boolean algebras of projections in Banach spaces

D. H. Fremlin, B. de Pagter, W. J. Ricker (2005)

Studia Mathematica

Similarity:

Complete and σ-complete Boolean algebras of projections acting in a Banach space were introduced by W. Bade in the 1950's. A basic fact is that every complete Boolean algebra of projections is necessarily a closed set for the strong operator topology. Here we address the analogous question for σ-complete Boolean algebras: are they always a sequentially closed set for the strong operator topology? For the atomic case the answer is shown to be affirmative. For the general case, we develop...

Compact Boolean algebras

Wiesław Głowczyński (2005)

Acta Universitatis Carolinae. Mathematica et Physica

Similarity:

On the injectivity of Boolean algebras

Bernhard Banaschewski (1993)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

The functor taking global elements of Boolean algebras in the topos 𝐒𝐡 𝔅 of sheaves on a complete Boolean algebra 𝔅 is shown to preserve and reflect injectivity as well as completeness. This is then used to derive a result of Bell on the Boolean Ultrafilter Theorem in 𝔅 -valued set theory and to prove that (i) the category of complete Boolean algebras and complete homomorphisms has no non-trivial injectives, and (ii) the category of frames has no absolute retracts.