Related papers: Sectional category and The Fixed Point Property

Using Gottschalk's notion\,---\,weakly locally almost periodic point, we show in this paper that if $f\colon X\rightarrow X$ is a minimal continuous transformation of a compact Hausdorff space $X$ to itself, then for all entourage…

We introduce a finiteness property for braided fusion categories, describe a conjecture that would characterize categories possessing this, and verify the conjecture in a number of important cases. In particular we say a category has F if…

In this paper we introduce FG- coupled fixed point, which is a generalization of coupled fixed point for nonlinear mappings in partially ordered complete metric spaces. We discuss existence and uniqueness theorems of FG- coupled fixed…

A simple criterion for a functor to be finitary is presented: we call $F$ finitely bounded if for all objects $X$ every finitely generated subobject of $FX$ factorizes through the $F$-image of a finitely generated subobject of $X$. This is…

Using methods from commutative algebra and topos-theory, we construct topos-theoretical points for the fppf topology of a scheme. These points are indexed by both a geometric point and a limit ordinal. The resulting stalks of the structure…

This paper is the second in a series exploring the properties of a functor which assigns a homotopy double groupoid with connections to a Hausdorff space. We show that this functor satisfies a version of the van Kampen theorem, and so is a…

We propose a fixed-point property for group actions on cones in topological vector spaces. In the special case of equicontinuous actions, we prove that this property always holds; this statement extends the classical Ryll-Nardzewski theorem…

Firmly nonexpansive mappings play an important role in metric fixed point theory and optimization due to their correspondence with maximal monotone operators. In this paper we do a thorough study of fixed point theory and the asymptotic…

Let F be a local net of von Neumann algebras in four spacetime dimensions satisfying certain natural structural assumptions. We prove that if F has trivial superselection structure then every covariant, Haag-dual subsystem B is the fixed…

For a metrizable space $X$ of density $\kappa$, let $PM(X)$ be the space of continuous bounded pseudometrics on $X$ endowed with the uniform convergence topology. In this paper, its topology shall be classified as follows: (i) If $X$ is…

In this paper, we introduce the notion of partially ordered {\epsilon}-chainable metric spaces and we derive new coupled fixed point theorems for uniformly locally contractive mappings on such spaces.

We establish two fixed point theorems for certain mappings of contractive type. The first result is concerned with the case where such mappings take a nonempty, closed subset of a complete metric space $X$ into $X$, and the second with an…

We study weak and strong solutions of nonlinear non-compact operator equations in abstract spaces of adapted random points. The main result of the paper is similar to Schauder's fixed-point theorem for compact operators. The illustrative…

Suppose that Q is a family of seminorms on a locally convex space E which determines the topology of E. We study the existence of Q-nonexpansive retractions for families of Q-nonexpansive mappings and prove that a separated and sequentially…

In this article, we derive a common fixed point result for a pair of single valued and set-valued mappings on a metric space having graphical structure. In this case, the set-valued map is assumed to be closed valued instead of closed and…

A space $X$ is "sequentially $n$-connected" at $x\in X$ if for every $0\leq k\leq n$ and sequence of maps $f_1,f_2,f_3,\dots:S^k\to X$ that converges toward a point $x\in X$, the maps $f_m$ contract by a sequence of null-homotopies that…

This paper seeks to advance the theory of nonexpansive mappings by introducing and exploring a novel class of nonexpansive type mappings, which we aptly designate as perimetric nonexpansive mappings. We establish that the collection of…

One of the important consequences of the Banach Fixed Point Theorem is Hutchinson's theorem which states the existence and uniqueness of fractals in complete metric spaces. The aim of this paper is to extend this theorem for semimetric…

We define a new class of symplectic objects called "stops", which roughly speaking are Liouville hypersurfaces in the boundary of a Liouville domain. Locally, these can be viewed as pages of a compatible open book. To a Liouville domain…

A space X is finite dimensional, locally compact and separable metrizable if and only if X has a finite basic family: continuous functions Phi_1,...,Phi_n of X to the reals, R, such that for all continuous f from X to R there are g_1,...,…