A new class of spaces with all finite powers Lindelof

TL;DR

This paper introduces 'iota spaces', a new class of topological spaces related to epsilon-spaces, and investigates their properties, including an example of a hereditarily epsilon-space with a non-Lindelof square.

Contribution

It defines 'iota spaces' based on a new class of open covers and explores their relationship with epsilon-spaces and countable network weight, providing new insights and examples.

Findings

Introduces 'iota spaces' and their defining properties.

Establishes relationships between 'iota spaces' and epsilon-spaces.

Provides an example of a hereditarily epsilon-space whose square is not hereditarily Lindelof.

Abstract

We consider a new class of open covers and classes of spaces defined from them, called "iota spaces". We explore their relationship with epsilon-spaces (that is, spaces having all finite powers Lindelof) and countable network weight. An example of a hereditarily epsilon-space whose square is not hereditarily Lindelof is provided.