A new class of spaces with all finite powers Lindelöf

We consider a new class of open covers and classes of spaces defined from them, called ι-spaces (“iota spaces”). We explore their relationship with ϵ-spaces (that is, spaces having all finite powers Lindelöf) and countable network weight. An example of a hereditarily ϵ-space whose square is not hereditarily Lindelöf is provided answering a question from [11].