Displaying similar documents to “On Cohen's theorem”

Combinatorics of ideals --- selectivity versus density

A. Kwela, P. Zakrzewski (2017)

Commentationes Mathematicae Universitatis Carolinae

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This note is devoted to combinatorial properties of ideals on the set of natural numbers. By a result of Mathias, two such properties, selectivity and density, in the case of definable ideals, exclude each other. The purpose of this note is to measure the ``distance'' between them with the help of ultrafilter topologies of Louveau.

When a unital F-algebra has all maximal left (right) ideals closed?

W. Żelazko (2006)

Studia Mathematica

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We prove that a real or complex unital F-algebra has all maximal left ideals closed if and only if the set of all its invertible elements is open. Consequently, such an algebra also automatically has all maximal right ideals closed.