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p-solid/liquid Abelian monoids?


Steve.Vickers
(@steve-vickers)
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[ 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.)

 

Steve.


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