Some basic results on pro-affine algebras and ind-affine schemes (Q1411273)

The first part of the paper studies topological and algebraic properties of a pro-affine algebra, that is of a countable topological \(k\)-algebra which is complete, separated and with a countable basis of 0-neighborhoods. Special attention is posed on open prime and open maximal ideals and a definition is given of radical and nilradical, generalizing the usual one. The second part of the paper deals with ind-schemes and ind-affine varieties, defined starting from ``open prime ideals'' and ``open maximal ideals'' instead of from the prime and maximal ideals of the classical situation. Some interesting examples are given.