Zobrazeno 1 - 10
of 65
pro vyhledávání: '"Francisco R. Ruiz"'
We give a combinatorial description of shape theory using finite topological $T_0$-spaces (finite partially ordered sets). This description may lead to a sort of computational shape theory. Then we introduce the notion of core for inverse sequences o
Externí odkaz:
http://arxiv.org/abs/2205.03034
We construct a category that classifies compact Hausdorff spaces by their shape and finite topological spaces by their weak homotopy type.
Externí odkaz:
http://arxiv.org/abs/2110.02574
Given a compact metric space $X$, we associate to it an inverse sequence of finite $T_0$ topological spaces. The inverse limit of this inverse sequence contains a homeomorphic copy of $X$ that is a strong deformation retract. We provide a method to a
Externí odkaz:
http://arxiv.org/abs/2107.11271
Publikováno v:
Fixed Point Theory and Applications, Vol 2010 (2010)
Let U⊂ℝ2 be an open subset and f:U→ℝ2 be an arbitrary local homeomorphism with Fix(f)={p}. We compute the fixed point indices of the iterates of f at p,iℝ2(fk,p), and we identify these indices in dynamical terms. Therefore, we obtain a sort
Externí odkaz:
https://doaj.org/article/add34dfae861407cbbbc1db3f554a98f
We prove that the unique possible flow in an Alexandroff $T_0$-space is the trivial one. To motivate this result, we relate Alexandroff spaces to topological hyperspaces.
Externí odkaz:
http://arxiv.org/abs/2104.00894
Let $f:G\rightarrow H$ be a homomorphism of groups, we construct a topological space $X_f$ such that its group of homeomorphisms is isomorphic to $G$, its group of homotopy classes of self-homotopy equivalences is isomorphic to $H$ and the natural ma
Externí odkaz:
http://arxiv.org/abs/2011.07257
We construct two planar homeomorphisms $f$ and $g$ for which the origin is a globally asymptotically stable fixed point whereas for $f \circ g$ and $g \circ f$ the origin is a global repeller. Furthermore, the origin remains a global repeller for the
Externí odkaz:
http://arxiv.org/abs/2010.12893
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 literature
Externí odkaz:
http://arxiv.org/abs/2010.12804
Autor:
Hernández-Corbato, Luis, Nieves-Rivera, David Jesús, Del Portal, Francisco R. Ruiz, Sánchez-Gabites, Jaime J.
Publikováno v:
Ergod. Th. Dynam. Sys. 40 (2020) 2434-2452
Let $X$ be a compact, metric and totally disconnected space and let $f:X\to X$ be a continuos map. We relate the eigenvalues of $f_{*}:\check{H}_{0}(X;\mathbb{C})\to\check{H}_{0}(X;\mathbb{C})$ to dynamical properties of $f$, roughly showing that if
Externí odkaz:
http://arxiv.org/abs/1807.08043
In this paper we study the cohomological Conley index of arbitrary isolated invariant continua for continuous maps $f \colon U \subseteq \mathbb{R}^d \to \mathbb{R}^d$ by analyzing the topological structure of their unstable manifold. We provide a si
Externí odkaz:
http://arxiv.org/abs/1802.02521