Related papers: A parametrized version of the Borsuk Ulam theorem

Checking whether a system of linear equations is consistent is a basic computational problem with ubiquitous applications. When dealing with inconsistent systems, one may seek an assignment that minimizes the number of unsatisfied…

For a finite group $H$ and connected topological spaces $X$ and $Y$ such that $X$ is endowed with a free left $H$-action $\tau$, we provide a geometric condition in terms of the existence of a commutative diagram of spaces (arising from the…

In this paper we study the existence and regularity of stable manifolds associated to fixed points of parabolic type in the differentiable and analytic cases, using the parametrization method. The parametrization method relies on a suitable…

Given $n$ distinct points $\mathbf{x}_1, \ldots, \mathbf{x}_n$ in $\mathbb{R}^d$, let $K$ denote their convex hull, which we assume to be $d$-dimensional, and $B = \partial K $ its $(d-1)$-dimensional boundary. We construct an explicit…

We introduce the notion of a symmetric group parametrized by elements of a group. We show that this group is an extension of a certain subgroup of the wreath product $G \wr S_n$ by $\mathrm{H}_2(G, \mathbb{Z})$. We also discuss the…

Dependence on the parameter is continuous when perturbations of the parameter preserves strict preference for one alternative over another. We characterise this property via a utility function over alternatives that depends continuously on…

Nearly all simulation-based games have environment parameters that affect incentives in the interaction but are not explicitly incorporated into the game model. To understand the impact of these parameters on strategic incentives, typical…

For a set-valued function $F$ on a compact subset $W$ of a manifold, spanning is a topological property that implies that $F(x) \ne 0$ for interior points $x$ of $W$. A myopic equilibrium applies when for each action there is a payoff whose…

In this paper, we address the longstanding question of whether expansive homeomorphisms can exist within convex bodies in Euclidean spaces. Utilizing fundamental tools from topology, including the Borsuk-Ulam theorem and Brouwer's…

We develop a minimal, timeless game-theoretic representation of the mass-geometry relation. An "Object" (mass) and "Space" (geometry) choose strategies in a static normal-form game; utilities encode stability as mutual consistency rather…

Let $(X,D)$ be a smooth log pair over $\mathbb{C}$ such that the complement $U := X \setminus D$ carries a maximally varied family of polarized manifolds. We prove a version of second main theorem on $(X,D)$ by using the Viehweg-Zuo…

The behavior of a class of mappings of a domain of Euclidean space is studied. It is established that the indicated class is equicontinuous both at the inner and at the boundary points of the domain if the mappings contained in it satisfy…

The Choquet - Bishop - de Leeuw theorem states that each element of a compact convex subset of a locally convex topological Hausdorff space is a barycenter of a probability measure supported by the set of extreme points of that set. By the…

We present the effective version of the theorem about turning Borel sets in Polish spaces into clopen sets while preserving the Borel structure of the underlying space. We show that under some conditions the emerging parameters can be…

We introduce a new topological invariant of complex line arrangements in the complex projective plane, derived from the interaction between their complement and the boundary of a regular neighbourhood. The motivation is to identify Zariski…

We derive analytic solutions for the potential and field in a one-dimensional system of masses or charges with periodic boundary conditions, in other words Ewald sums for one dimension. We also provide a set of tools for exploring the…

In this paper we study analytic families of degree 2 parabolic-like mappings (as we defined in arXiv:1111.7150). We prove that the corresponding family of hybrid conjugacies induces a continuous map, which associates to each parameter the…

We prove that in a certain class E of nonseparable Banach spaces the norm topology of the dual ball is definable in terms of its weak* topology. Thus, any weak* homeomorphism between duals balls of spaces in E is automatically…

For nearly three decades, spatial games have produced a wealth of insights to the study of behavior and its relation to population structure. However, as different rules and factors are added or altered, the dynamics of spatial models often…

Results on continuous dependence on parameters, as well as on regularization, of solutions to linear systems of parabolic partial differential equations of second order with delay are given. One of the main features is that the topology on…