Products of spaces with countable $k$-network

[Moniker1998]

This is a new meta-property, and it establishes that square of one-point compactification of $\mathbb{Q}$ has countable $k$-network.

[prabau]

The justification in T. Banakh's answer uses the fact from Alas-Wilson that
[ compact + hereditarily Lindelof => sequentially compact ].

To make things complete, we should add this theorem also.

[yhx-12243]

The justification in T. Banakh's answer uses the fact from Alas-Wilson that [ compact + hereditarily Lindelof => sequentially compact ].

To make things complete, we should add this theorem also.

This is #1551.

[prabau]

Thanks. I'll review the other PR first then.

[Moniker1998]

I've added same metaproperty to countable networks, without justification since that one is easy

[Moniker1998]

@prabau you wanted to review this PR next

[prabau]

I read the proof of Banakh, nice result. Will check this PR in particular later today.