# A direct solution to the Generic Point Problem

## TL;DR

This paper offers a new proof demonstrating that for certain Polish groups and minimal flows with meager orbits, the universal minimal flow is inherently non-metrizable, highlighting a fundamental property of these mathematical structures.

## Contribution

It provides a direct proof of a recent theorem relating to the non-metrizability of universal minimal flows for specific Polish groups and flows.

## Key findings

- Universal minimal flow $M(G)$ is non-metrizable under given conditions.
- Universal highly proximal extension of certain flows is non-metrizable.
- The proof offers a new perspective on the structure of minimal flows.

## Abstract

We provide a new proof of a recent theorem of Ben-Yaacov, Melleray, and Tsankov. If $G$ is a Polish group and $X$ is a minimal, metrizable $G$-flow with all orbits meager, then the universal minimal flow $M(G)$ is non-metrizable. In particular, we show that given $X$ as above, the universal highly proximal extension of $X$ is non-metrizable.