Property Suggestion: Punctiform

[Moniker1998]

Property Suggestion

A space is said to be Punctiform provided it doesn't contain a non-degenerate continuum.

There seems to be some discussion as to if we should assume continua are Hausdorff in this definition.

Rationale

This property appears in Engelking.

Relationship to other properties

Has a dispersion point + Hausdorff => Punctiform

[prabau]

That's very classical, worth having I think. It's probably detailed in Kuratowski's books.

Non-degenerate = with at least two points ?

[Moniker1998]

@prabau yeah

[Moniker1998]

@prabau I found this property in Engelking, particularly, Engelking asks to show that the Knaster-Kuratowski space is punctiform. I've noticed, this is actually automatic if you have a dispersion point.

[prabau]

Actually, I don't see immediately why has a dispersion point + T2 => punctiform. I'll see it when you write a PR, or you'll reference something I suppose.

[Moniker1998]

@prabau https://math.stackexchange.com/a/5127080/476484 I've added a comment to my answer here. See the corollary
I don't guarantee I'll be writing a PR for this by the way