Abstract In this paper we propose a basic fixed-point theorem for correspondences inspired by Tarski’s intersection point theorem. This result furnishes an efficient tool to prove the existence of pure strategy Nash equilibria two player games with possibly discontinuous payoffs functions defined on compact real intervals.

Based on Nakajima’s Classification Theorem [N] we describe the precise form of the binomial equations which determine toric locally complete intersection (“l.c.i”) singularities.

We obtain a number of consequences of the theorem on the automatic continuity of locally bounded finite-dimensional representations of connected Lie groups on the derived subgroup of the group, as well as an analogue of Lie’s theorem for (not necessarily continuous) finite-dimensional representations of connected soluble locally compact groups. In particular, we give a description of connected ...

Cost functions in problems concerning the existence of Nash Equilibria are traditionally multilinear in the mixed strategies. The main aim of this paper is to relax the hypothesis of multilinearity. We use basic intersection theory, Poincaré Duality and the Dold-Thom Theorem to establish existence of Nash Equilibria under fairly general topological hypotheses. The Dold-Thom Theorem provides us ...

This paper presents an executable semantics of OO models. We made it possible to conduct both simulation and theorem proving on the semantics by implementing its underlying heap memory structure within the expressive intersection of the functional language ML and the theorem prover HOL. This paper also presents a verification system ObjectLogic which supports simulation and theorem proving of O...

We give a new proof of Delsarte, Goethals and Mac williams theorem on minimal weight codewords of generalized Reed-Muller codes published in 1970. To prove this theorem, we consider intersection of support of minimal weight codewords with affine hyperplanes and we proceed by recursion.

We prove a “Tverberg type” multiple intersection theorem. It strengthens the prime case of the original Tverberg theorem from 1966, as well as the topological Tverberg theorem of Bárány et al. (1980), by adding color constraints. It also provides an improved bound for the (topological) colored Tverberg problem of Bárány & Larman (1992) that is tight in the prime case and asymptotically optimal ...