p-solid/liquid Abelian monoids?
[ Sorry if this was already covered in the talk. I stupidly overlooked the time difference, so I’ve had to catch up with the “Liquid tensor experiment” notes https://xenaproject.wordpress.com/2020/12/05/liquid-tensor-experiment/ ]
The definition of solid Abelian group in the notes uses signed measures. If you use non-negative measures, do you usefully get a similar notion of solid Abelian monoid?
(I’m interested in understanding how far the notions for condensed sets transfer to point-free topological spaces. For them we have some decent notions of measure and integration, but you have to be much more careful about whether reals are Dedekind or 1-sided, and that makes subtraction delicate.
By the way, Ming Ng’s talk this afternoon includes suggestions that the scaling factor p from Ostrowski’s theorem in the Archimedean case is best considered as an upper real, ie with the topology of upper semicontinuity.)