Liquid Vector Space
The concept of a liquid vector space is part of condensed mathematics. Liquid vector spaces are an alternative to topological vector space In mathematics, a topological vector space (also called a linear topological space and commonly abbreviated TVS or t.v.s.) is one of the basic structures investigated in functional analysis. A topological vector space is a vector space that is als ...s. References Vector spaces {{math-stub ...
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Condensed Mathematics
Condensed mathematics is a theory developed by and Peter Scholze which, according to some, aims to unify various mathematical subfields, including topology, complex geometry, and algebraic geometry. Idea The fundamental idea in the development of the theory is given by replacing topological 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. In particular, unlike the category of topological abelian groups, the category of condensed abelian groups is an abelian category, which allows for the use of tools from homological algebra in the study of those structures. The framework of condensed mathematics turns out to be general enough that, by considering various "spaces" with sheaves valued in condensed algebras, one is able to incorporate algebraic geometry, p-adic analytic geometry and complex analytic geometry. Def ...
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