Non-meager $P$-filters are Countable Dense Homogeneous

TL;DR

The paper proves that non-meager P-filters and their countable product spaces are countable dense homogeneous, revealing a significant topological property of these filters.

Contribution

It establishes that non-meager P-filters and their countable powers are countable dense homogeneous spaces, a novel topological characterization.

Findings

Non-meager P-filters are countable dense homogeneous.

Their countable product spaces also exhibit countable dense homogeneity.

Provides new insights into the topological structure of P-filters.

Abstract

We prove that if $\mathcal{F}$ is a non-meager $P$-filter, then both $\mathcal{F}$ and ${}^\omega\mathcal{F}$ are countable dense homogeneous spaces.