Any nonempty, compact, semi-algebraic set in [0, 1]n is the projection of the set of mixed equilibria of a finite game with 2 actions per player on its first n coordinates. A similar result follows for sets of equilibrium payoffs. The proofs are constructive and elementary.

The notion of a tensor product of topological groups and modules is important in theory of topological groups, algebraic number theory. The tensor product of compact zero-dimensional modules over a pseudocompact algebra was introduced in [B] and for the commutative case in [GD], [L]. The notion of a tensor product of abelian groups was introduced in [H]. The tensor product of modules over commu...

We construct low cardinality admissible meshes for polynomials on three classes of planar compact domains: cartesian graph domains, polar graph domains, and domains with piecewise C 2 boundary, that satisfy a Markov polynomial inequality. 1 Planar cartesian and polar graph domains Let K ⊂ R d be a polynomial determining compact domain (i.e., a polynomial vanishing there vanishes everywhere). We...

It will be convenient to call a space X a ParoviZenko space if (cy) X is a zero-dimensional compact space without isolated points, (p) every two disjoint open F,-sets have disjoint closures, and (y) every nonempty GG-set in X has non-empty interior. Compact spaces satisfying (p) are usually called F-spaces, while spaces satisfying (y) are called almost-P spaces. Examples of F-spaces are the ext...

This paper characterizes which subsets of Cn can be the set of positions of n points on a linkage in C. For example, assuming compactness they are just compact semialgebraic sets. Noncompact configuration spaces are semialgebraics sets invariant under the Euclidean group, with compact quotient.

In this paper we study the local behaviour of admissible metrics in the kYamabe problem on compact Riemannian manifolds (M, g0) of dimension n ≥ 3. For n/2 < k < n, we prove a sharp Harnack inequality for admissible metrics when (M, g0) is not conformally equivalent to the unit sphere S and that the set of all such metrics is compact. When (M,g0) is the unit sphere we prove there is a unique ad...

Let (M, g) be a compact Riemannian manifold of dimension N ≥ 5 and Qg be its Q curvature. The prescribed Q curvature problem is concerned with finding metric of constant Q curvature in the conformal class of g. This amounts to finding a positive solution to Pg(u) = cu N+4 N−4 , u > 0 on M where Pg is the Paneitz operator. We show that for dimensions N ≥ 25, the set of all positive solutions to ...

I. Contractible manifolds and aspherical manifolds. Suppose that M n is a compact, contractible n-manifold with boundary. These assumptions imply that the boundary of M has the homology of an (n-l)-sphere; however, they do not imply that it is simply connected. If n ~ 3, then for M n to be homeomorphic to a disk it is obviously necessary that ~M be simply connected. For n ~ 5 this condition is ...

The aim of this paper is to establish some relationship between the set strong uniform statistical cluster points and a given sequence in probabilistic normed space. To aim, let density be on positive integers N for space, that is, cases as equal lower upper subset N. We introduce concept give new type convergence Note non-empty compact set. also investigate properties all