# Internal characterizations of productively Lindel\"of spaces

## TL;DR

This paper provides an internal characterization of productively Lindel"of spaces, resolving a longstanding problem and exploring their relation to Alster spaces.

## Contribution

It introduces a new internal criterion for identifying productively Lindel"of spaces and compares these spaces with Alster spaces.

## Key findings

- Established an internal characterization for productively Lindel"of spaces.
- Resolved a long-standing problem attributed to Tamano.
- Explored the relationship between Alster spaces and productively Lindel"of spaces.

## Abstract

We present an internal characterization for the productively Lindel\"of property, thus answering a long-standing problem attributed to Tamano. We also present some results about the relation Alster spaces vs. productively Lindel\"of spaces.