On this Wikipedia the language links are at the top of the page across from the article title. The fundamental idea in the development of the theory is given by replacing condensed milk recipes spaces by condensed sets, defined below. The category of condensed sets, as well as related categories such as that of condensed abelian groups, are much better behaved than the category of topological spaces.

A condensed set is a sheaf of sets on the site of profinite sets, with the Grothendieck topology given by finite, jointly surjective collections of maps. Similarly, a condensed group, condensed ring, etc. In 2013, Bhargav Bhatt and Peter Scholze introduced a general notion of pro-étale site associated to an arbitrary scheme. In 2020 Scholze has completed a proof of a result which would enable to incorporate functional analysis as well as complex geometry into the condensed mathematics framework, using the notion of liquid vector spaces. Coincidentally, in 2019 Barwick and Haine have introduced a very similar theory of pyknotic objects.

This theory is very closely related to that of condensed sets, with the main differences being set-theoretic in nature: pyknotic theory depends on a choice of Grothendieck universes, whereas condensed mathematics can be developed strictly within ZFC. Half a year of the Liquid Tensor Experiment: Amazing developments”. See definition of condensed on Dictionary. 2013 by the Philip Lief Group. See how your sentence looks with different synonyms.

Devise Dithyrambs With Help From This Word Of The Day Quiz! University of the Basque Country in Spain who was not involved in the work. On this Wikipedia the language links are at the top of the page across from the article title. Condensation is the change of state of matter from a gas phase into a liquid phase.