A characterization of productive cellularity

TL;DR

This paper explores the concept of productive cellularity in posets and topological spaces, providing criteria to identify when these structures are productively ccc, which is important for understanding their combinatorial and topological properties.

Contribution

It introduces necessary and sufficient conditions for a poset or topological space to be productively ccc, advancing the theoretical understanding of cellularity in these structures.

Findings

Characterization of productive cellularity in posets and topological spaces

Criteria for a space to be productively ccc

Application of antichain families ordered by reverse inclusion

Abstract

We investigate the notion of productive cellularity of arbitrary posets and topological spaces. Particularly, by working with families of antichains ordered with reverse inclusion, we give necessary and sufficient conditions to determine whether a poset or a topological space is productively ccc.