Knaster-Kuratowski fan S125 has fixed point property

[prabau]

The Knaster-Kuratowski fan (S125) has the fixed point property (P89).

[Moniker1998]

@prabau you have checked the result?

[prabau]

@prabau you have checked the result?

Yes, I checked it.

[Moniker1998]

@prabau do you know if conjecture 1 is open?

[Moniker1998]

@prabau should we add property "has explosion points"? It seems like the conjecture is true for those, and open for dispersion points

[prabau]

@prabau should we add property "has explosion points"? It seems like the conjecture is true for those, and open for dispersion points

Maybe, but not sure it's a very notable property. We would have to discuss in an issue, find example spaces that have a dispersion point that is not an explosion point, etc. And also check if the terminology is consistent in the literature. These connectedness related properties seem to have a lot of variations.

https://zbmath.org/1101.54041 seems to show Conjecture 1 is false even for explosion points.

[Moniker1998]

@prabau I think it would be nice to add, if only for the fact that it helps us to distinguish between spaces, and it exists in the literature. Could you add the explosion points property to the "issues" page (not necessarily right now, but after this PR is over)?

[Moniker1998]

@prabau do you want me to read the paper before I approve this? I will read it eventually, but I need to catch up on the proof of connectedness of Knaster-Kuratowski space and so on as well.
Since you've already read it, there seems to be no need

[Moniker1998]

@prabau by the way we should add Dijkstra's space, can you add an issue about it

[prabau]

@prabau do you want me to read the paper before I approve this? I will read it eventually, but I need to catch up on the proof of connectedness of Knaster-Kuratowski space and so on as well. Since you've already read it, there seems to be no need

I have read the paper and am confident in its validity. But feel free to read it yourself as well if you are interested. There is no rush in approving this PR. It's fine if it takes a few weeks more. Up to you.

[prabau]

@prabau I think it would be nice to add, if only for the fact that it helps us to distinguish between spaces, and it exists in the literature. Could you add the explosion points property to the "issues" page (not necessarily right now, but after this PR is over)?

We could possibly have it in the future, but I am not pushing for it, so I will not add such an issue right now. Actually, I think we already have so many pending issues that nobody is working on. If someone really cares about it and plans to work on it, they can write it at any time.

[Moniker1998]

@prabau I've added those issues myself. You can to them if you want. Also, feel free to merge this