Related papers: Homological selections and fixed-point theorems
Characterizations of paracompact finite $C$-spaces via continuous selections are given. We apply these results to obtain some properties of finite $C$-spaces. Factorization theorems and a completion theorem for finite $C$- spaces are also…
A topological space has the fixed point property if every continuous self-map of that space has at least one fixed point. We demonstrate that there are serious restraints imposed by the requirement that there be a choice of fixed points…
The fixed-point theory and its applications to various areas of science are well known. In this paper we present some existence and uniqueness theorems for fixed circles of self-mappings on metric spaces with geometric interpretation. We…
We adapt the definition of the Vietoris map to the framework of finite topological spaces and we prove some coincidence theorems. From them, we deduce a Lefschetz fixed point theorem for multivalued maps that improves recent results in the…
In this paper we prove some new fixed point theorems for multivalued mappings on orbitally complete uniform spaces.
We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.
The paper contains a very simple proof of the classical Hasumi's theorem that each usco mapping defined on an extremally disconnected space has a continuous selection. The paper also contains a very simple proof of a recent result about…
We establish a fixed-point theorem for the face maps that consist in deleting the $i$th entry of an ordered set. Furthermore, we show that there exists random finite sets of integers that are almost invariant under such deletions.…
We survey several applications of fixed point theorems in the theory of invariant subspaces. The general idea is that a fixed point theorem applied to a suitable map yields the existence of invariant subspaces for an operator on a Banach…
New fixed point results are presented for ${\cal U}_c^{\kappa}(X,X)$ maps in extension type spaces.
We present a fixed point theorem on topological cylinders in normed linear spaces for maps satisfying a property of stretching a space along paths. This result is a generalization of a similar theorem obtained by D. Papini and F. Zanolin.…
The concept of quasi-partial b-metric-like spaces is being introduced and studied with the help of topology. Examples are also discussed to support the results. Some fixed point theorems are proved in the setting of quasi-partial…
In this paper, vector ultrametric spaces are introduced and a fixed point theorem is given for correspondences. Our main result generalizes a known theorem in ordinary ultrametric spaces.
Persistent homology is a popular and useful tool for analysing finite metric spaces, revealing features that can be used to distinguish sets of unlabeled points and as input into machine learning pipelines. The famous stability theorem of…
The purpose of this paper is to present some multidimensional fixed-point theorems and their applications. For this, we provide a multidimensional fixed point theorem and then using this theorem we prove the existence and uniqueness of a…
The goal of this paper is to establish a general fixed point theorem for compact single-valued continuous mapping in Hausdorff p-vector spaces, and the fixed point theorem for upper semicontinuous set-valued mappings in Hausdorff locally…
In this paper, we introduce the concept of quasi-point-separable topological vector spaces, which has the following important properties: 1.In general, the conditions for a topological vector space to be quasi-point-separable is not very…
In this paper a generalized topological central point theorem is proved for maps of a simplex to finite-dimensional metric spaces. Similar generalizations of the Tverberg theorem are considered.
We establish the first common fixed point theorem for commutative set-valued mappings. This may help to generalize common fixed point theorems in single-valued setting to those in set-valued. We also prove the existence of a fixed point in…
Uniformly finite homology is a coarse invariant for metric spaces; in particular, it is a quasi-isometry invariant for finitely generated groups. In this article, we study uniformly finite homology of finitely generated amenable groups and…