Add P219 Toronto

[StevenClontz]

No description provided.

[Moniker1998]

@StevenClontz is this a meme draft?

[StevenClontz]

Admittedly, @ccaruvana @lyengulalp @jocelynbell and others did put this together with me at the SumTopo banquet dinner, as a bit.

It can be ignored for now, but I think it would make a legitimate contribution after some polish. It is discussed in e.g. Open Problems in Topology pg 15. Whether we include the "rules" for discussing the Toronto problem is up for debate I suppose. (They don't belong as meta-properties of course.)

[prabau]

Yeah, I was wondering if this was a "joke" property.

But, has this notion received enough attention with some interesting results/spaces to be worth including in pi-base?

[StevenClontz]

The latest commit provides the motivation: it's open whether in ZFC there exist uncountable non-discrete Toronto spaces.

[prabau]

https://mathoverflow.net/questions/24144/is-there-an-uncountable-non-discrete-hausdorff-toronto-space

https://en.wikipedia.org/wiki/Toronto_space

[StevenClontz]

So this search would be the Toronto problem: https://topology.pi-base.org/spaces?q=%7ECountable%2B%7EDiscrete%2BHausdorff%2BToronto (I forgot Hausdorff earlier)

To make this a serious PR, I need to add relevant facts about Toronto: it's implied by discrete and indiscrete, it's satsified by co-finite topologies, etc.

[prabau]

From the mo post above: "Under GCH the only Hausdorff Toronto spaces (of any cardinality) are the discrete spaces."

So there won't be any non-discrete Hausdorff example in ZFC.

[prabau]

Lots of great stuff in W. Brian, "The Toronto problem" https://zbmath.org/1286.54032

[Moniker1998]

@StevenClontz are you going to work on this PR?