Spaces with -weakly hereditarily closure-preserving sn-networks.
Quasi -spaces are defined to be those Tychonoff spaces such that each prime -ideal of is either minimal or maximal. This article is devoted to a systematic study of these spaces, which are an obvious generalization of -spaces. The compact quasi -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 -spaces is given. If is a cozero-complemented space and every nowhere dense zeroset...
Motivated by some examples, we introduce the concept of special almost P-space and show, using the reflection principle, that for every space of this kind the inequality “" holds.
We present a new method for establishing the ‘‘gap” property for finitely generated subgroups of , providing an elementary solution of Ruziewicz problem on as well as giving many new examples of finitely generated subgroups of with an explicit gap. The distribution of the eigenvalues of the elements of the group ring in the -th irreducible representation of is also studied. Numerical experiments indicate that for a generic (in measure) element of , the “unfolded” consecutive spacings...
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...