SPM Bulletin 24

TL;DR

This bulletin compiles recent research on topological games, set theory, metric spaces, embeddings, measure theory, and properties of topologies, highlighting advances across various areas of mathematical logic and topology.

Contribution

It provides a curated overview of current developments and open problems in topology, set theory, and related fields, emphasizing new results and classifications.

Findings

Topological games and their properties analyzed

Universal Baire property for sigma^1_2 sets studied

Linearity of sigma-additivity in Scheepers Diagram properties

Abstract

1. A Wikipedia entry on topological games 2. On a fragment of the universal Baire property for sigma^1_2 sets 3. The coarse classification of homogeneous ultra-metric spaces 4. Ramsey-like embeddings 5. Proper and piecewise proper families of reals 6. Measures and their random reals 7. Obtainable Sizes of Topologies on Finite Sets 8. Spaces of R-places of rational function fields 9. All properties in the Scheepers Diagram are linearly-sigma-additive.