Preserving the Lindel\"of property under forcing extensions

TL;DR

This paper explores conditions under which various strengthened forms of the Lindel"of property in topological spaces are preserved when extending models via forcing, including indestructibility and Rothberger properties.

Contribution

It provides new sufficient conditions for preserving the Lindel"of property and its strengthenings under forcing extensions.

Findings

Identifies conditions preserving indestructible Lindel"of property

Establishes criteria for Rothberger property preservation

Analyzes preservation of Lindel"of P-spaces

Abstract

We investigate preservation of the Lindel\"of property of topological spaces under forcing extensions. We give sufficient conditions for a forcing notion to preserve several strengthenings of the Lindel\"of property, such as indestructible Lindel\"of property, the Rothberger property and being a Lindel\"of P-space.