# SPM Bulletin 28

## TL;DR

The bulletin compiles recent research announcements and discussions on various topics in set theory, topology, and related areas, highlighting new results, open problems, and theoretical developments.

## Contribution

It presents a collection of new research findings, conjectures, and open problems across multiple areas in mathematical logic and topology.

## Key findings

- Introduction of ultrafilters with property (s)
- Results on Banach's Fixed Point Theorem converse
- Advances in stationary reflection and coloring theorems

## Abstract

Contents: 1. Editor's note; 2. gamma-sets from a weak hypothesis; 3. Research announcements; 3.1. Ultrafilters with property (s); 3.2. On a converse to Banach's Fixed Point Theorem; 3.3. Analytic groups and pushing small sets apart 3.4. Club-guessing, stationary reflection, and coloring theorems; 3.5. More on the pressing down game; 3.6. A note on discrete sets; 3.7. Antidiamond principles and topological applications; 3.8. Partitions and indivisibility properties of countable dimensional vector spaces; 3.9. Group-valued continuous functions with the topology of pointwise convergence; 3.10. Stationary and convergent strategies in Choquet games; 3.11. Linear sigma-additivity and some applications; 4. Unsolved problems from earlier issues.