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Spaces X in which all prime z -ideals of C ( X ) are minimal or maximal

Melvin Henriksen, Jorge Martinez, Grant R. Woods (2003)

Commentationes Mathematicae Universitatis Carolinae

Quasi P -spaces are defined to be those Tychonoff spaces X such that each prime z -ideal of C ( X ) is either minimal or maximal. This article is devoted to a systematic study of these spaces, which are an obvious generalization of P -spaces. The compact quasi P -spaces are characterized as the compact spaces which are scattered and of Cantor-Bendixson index no greater than 2. A thorough account of locally compact quasi P -spaces is given. If X is a cozero-complemented space and every nowhere dense zeroset...

Special almost P-spaces

Alessandro Fedeli (1997)

Commentationes Mathematicae Universitatis Carolinae

Motivated by some examples, we introduce the concept of special almost P-space and show, using the reflection principle, that for every space X of this kind the inequality “ | X | ψ c ( X ) t ( X ) " holds.

Special sets of reals and weak forms of normality on Isbell--Mrówka spaces

Vinicius de Oliveira Rodrigues, Victor dos Santos Ronchim, Paul J. Szeptycki (2023)

Commentationes Mathematicae Universitatis Carolinae

We recall some classical results relating normality and some natural weakenings of normality in Ψ -spaces over almost disjoint families of branches in the Cantor tree to special sets of reals like Q -sets, λ -sets and σ -sets. We introduce a new class of special sets of reals which corresponds to the corresponding almost disjoint family of branches being 0 -separated. This new class fits between λ -sets and perfectly meager sets. We also discuss conditions for an almost disjoint family 𝒜 being potentially...

Spectra of elements in the group ring of SU(2)

Alex Gamburd, Dmitry Jakobson, Peter Sarnak (1999)

Journal of the European Mathematical Society

We present a new method for establishing the ‘‘gap” property for finitely generated subgroups of SU ( 2 ) , providing an elementary solution of Ruziewicz problem on S 2 as well as giving many new examples of finitely generated subgroups of SU ( 2 ) with an explicit gap. The distribution of the eigenvalues of the elements of the group ring 𝐑 [ SU ( 2 ) ] in the N -th irreducible representation of SU ( 2 ) is also studied. Numerical experiments indicate that for a generic (in measure) element of 𝐑 [ SU ( 2 ) ] , the “unfolded” consecutive spacings...

Spectral Calculus and Lipschitz Extension for Barycentric Metric Spaces

Manor Mendel, Assaf Naor (2013)

Analysis and Geometry in Metric Spaces

The metric Markov cotype of barycentric metric spaces is computed, yielding the first class of metric spaces that are not Banach spaces for which this bi-Lipschitz invariant is understood. It is shown that this leads to new nonlinear spectral calculus inequalities, as well as a unified framework for Lipschitz extension, including new Lipschitz extension results for CAT (0) targets. An example that elucidates the relation between metric Markov cotype and Rademacher cotype is analyzed, showing that...

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