We consider the problem of the semidefinite representation of a class of non-compact basic semialgebraic sets. We introduce the conditions of pointedness and closedness at infinity of a semialgebraic set and show that under these conditions our modified hierarchies of nested theta bodies and Lasserre’s relaxations converge to the closure of the convex hull of S. Moreover, if the PP-BDR property...

In the paper, we describe various applications of the closedness and duality theorems of [7] and [8]. First, the strong separability of a polyhedron and a linear image of a convex set is characterized. Then, it is shown how stability conditions (known from the generalized Fenchel-Rockafellar duality theory) can be reformulated as closedness conditions. Finally, we present a generalized Lagrange...

Abrams’ theorem describes a necessary and sufficient condition for the closedness of a linear image of an arbitrary set. Closedness conditions of this type play an important role in the theory of duality in convex programming. In this paper we present generalizations of Abrams’ theorem, as well as Abrams-type theorems characterizing other properties (such as relatively openness or polyhedrality...

We investigate the frame properties and closedness for the shift invariant space

We introduce the class of linearly S-closed spaces as a proper subclass H-closed spaces. This property lies between S-closedness and countable S-closedness. A space is called if only any semi-open chain cover posses member dense in space. It shown that extremally disconnected coincide. gave characterizations these terms s-accumulation points filter bases complete families open subsets. While re...

Let K:=(K;+,⋅,D,0,1) be a differentially closed field of characteristic 0 with constants C. In the first part paper we explore connection between Ax-Schanuel type theorems (predimension inequalities) for differential equation E(x,y) and geometry fibres Us:={y:E(s,y)∧y∉C} where s is non-constant element. We show that certain types predimension inequalities imply strong minimality geometric trivi...

We prove the Existential Closedness conjecture for differential equation of j j -function and its derivatives. It states that in a differentia...

Let G G be a finitely presented group, and let H"> H encoding="application/x-tex">H subgroup of </inl...