Grothendieck groups, convex cones and maximal Cohen–Macaulay points

Sagbi Basis of Permutation Groups and Convex Cones

Rough convex cones and rough convex fuzzy cones

Based on the equivalence relation on a linear space, in this paper we introduce the definition of rough convex cones and rough convex fuzzy cones and discuss some of the fundamental properties of such rough convex cones.

Coincidence points and maximal elements of multifunctions on convex spaces

Generalized and unified versions of coincidence or maximal element theorems of Fan, Yannelis and Prabhakar, Ha, Sessa, Tarafdar, Rim and Kim, Mehta and Sessa, Kim and Tan are obtained. Our arguments are based on our recent works on a broad class of multifunctions containing composites of acyclic maps defined on convex subsets of Hausdorff topological vector spaces.

Bornological Completion of Locally Convex Cones

In this paper, firstly, we obtain some new results about bornological convergence in locally convex cones (which was studied in [1]) and then we introduce the concept of bornological completion for locally convex cones. Also, we prove that the completion of a bornological locally convex cone is bornological. We illustrate the main result by an example.

Weil and Grothendieck Approaches to Adelic Points

In [We, Ch. 1], Weil defines a process of “adelization” of algebraic varieties over global fields. One aim of this (largely) expository note is to prove for schemes of finite type over such fields (i.e., without affineness hypotheses), and even for separated algebraic spaces of finite type, that Weil’s adelization process coincides with the set of adelic points in the sense of Grothendieck on t...