Person:
Alonso Morón, Manuel

First Name

Manuel

Last Name

Alonso Morón

URI

https://hdl.handle.net/20.500.14352/75730

Affiliation

Universidad Complutense de Madrid

Faculty / Institute

Ciencias Matemáticas

Department

Álgebra, Geometría y Topología

Area

Geometría y Topología

Identifiers

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Now showing 1 - 10 of 58

On the Wallman-Frink compactification of 0-dimensional spaces and shape
(Archiv der Mathematik, 1992) Alonso Morón, Manuel
Here SF denotes the category whose objects are the pairs (X,P)where P is a metrizable ANR-space and X is a closed subset of P, and the morphisms between two objects (X,P) and (Y,Q) are the homotopy classes of mutations f:U(X,P)→V(Y,Q) (where U(X,P) and V(Y,Q) are the complete open neighborhood systems of X in P and Y in Q respectively). So two objects of SF are isomorphic if and only if they have the same shape in the sense of Fox (or Marde sic). The author constructs a covariant functor T from SF to the category C0 of all compact 0-dimensional spaces and continuous maps. This functor allows him to obtain new shape invariants in the class of metrizable spaces. Using this functor T he also constructs new contravariant functors to the the category of metrizable spaces and continuous maps and to the category of groups and homomorphisms. In order to construct T he uses the space of quasicomponents QX of a metrizable space X . Actually he uses the 0-dimensional compactification β0(QX) of QX. The space β0(QX) can be viewed as the 0-dimensional analogue of the Stone-Cech compactification. As a theorem he proves that two 0-dimensional metrizable spaces are of the same shape if and only if they are homeomorphic. This is a generalization in the metric case of a similar result for paracompacta due to G. Kozlowski and the reviewer [Fund. Math. 83 (1974), no. 2, 151-154] because there are metrizable spaces X such that ind(X)=0 but the covering dimension dim(X)>0 .
Aplicaciones cerradas y espacios en los que componentes y cuasicomponentes coinciden
(Contribuciones matemáticas. Libro-homenaje al profesor D. José Javier Etayo Miqueo, 1994) Cuchillo Ibáñez, Eduardo; Alonso Morón, Manuel; Romero Ruiz Del Portal, Francisco
This interesting and well-written survey article is devoted to the class P of topological spaces in which components and quasi-components coincide. This class includes the compact Hausdorff spaces and the locally connected spaces. It also includes every subset of the real line but not every subset of the plane. This class is closed under homotopy type, but the authors state that "it does not seem to be possible to give easily-stated conditions'' for membership in P . They do give some sufficient conditions using the fact that, to any topological space X , one can associate the quotient space ΔX in which each quasi-component is identified to a point (they show that this association is categorically natural). These conditions include the assumption that the quotient map is closed. For example, they show that, if X is normal and ΔX is zero-dimensional, then X∈P . Variations of this include the result that, if ΔX is zero-dimensional and the quasi-components are compact, then X∈P , and the result that, if X is locally compact Lindelöf and Hausdorff, then X∈P . No proofs are given. Can the fact that P is closed under homotopy equivalence be improved by allowing a more arbitrary homotopy index set (or not using a product structure at all)? What is an example of a space X whose quotient map is closed but X∉P ?
A combinatorial description of shape theory
() Chocano Feito, Pedro José; Alonso Morón, Manuel; Romero Ruiz Del Portal, Francisco
We give a combinatorial description of shape theory using finite topological T0-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 of finite spaces and prove some properties.
A note about the shape of attractors of discrete semidynamical systems
(Proceedings of the American Mathematical Society, 2006) Romero Ruiz Del Portal, Francisco; Alonso Morón, Manuel
We state in a short way a result that improves one of the main theorems in a paper of M. Gobbino concerning the topological properties that the phase space induces in an attractor of a discrete dynamical system.
A note on isomorphic groups and nonhomeomorphic spaces
(Acta Mathematica Hungarica, 1999) Cuchillo Ibáñez, Eduardo; Alonso Morón, Manuel; Romero Ruiz Del Portal, Francisco
Given a Tychonov space X we can construct another space Y with the same group of homeomorphisms such that X and Y are: in some sense, "almost arbitrarily different".
Bivariate delta-evolution equations and convolution polynomials: Computing polynomial expansions of solutions
(Applied Mathematics and Computation, 2011) Alonso Morón, Manuel; Luzón, Ana
This paper describes an application of Rota and collaborator's ideas, about the foundation on combinatorial theory, to the computing of solutions of some linear functional partial differential equations. We give a dynamical interpretation of the convolution families of polynomials. Concretely, we interpret them as entries in the matrix representation of the exponentials of certain contractive linear operators in the ring of formal power series. This is the starting point to get symbolic solutions for some functional-partial differential equations. We introduce the bivariate convolution product of convolution families to obtain symbolic solutions for natural extensions of functional-evolution equations related to delta-operators. We put some examples to show how these symbolic methods allow us to get closed formulas for solutions of genuine partial differential equations. We create an adequate framework to base theoretically some of the performed constructions and to get some existence and uniqueness results.
A topology for the sets of shape morphisms
(Topology and its Applications, 1999) Cuchillo Ibáñez, Eduardo; Alonso Morón, Manuel; Romero Ruiz Del Portal, Francisco; Rodríguez Sanjurjo, José Manuel
We introduce a topology on the set of shape morphisms between arbitrary topological spaces X, Y, Sh(X, Y). These spaces allow us to extend, in a natural way, some classical concepts to the realm of topological spaces. Several applications are given to obtain relations between shape theory and N-compactness and shape-theoretic properties of the spaces of quasicomponents.
C0-coarse geometry of complements of Z-sets in the Hilbert cube
(Transactions of the American Mathematical Society, 2008) Cuchillo Ibáñez, Eduardo; Dydak, J.; Koyama, A.; Alonso Morón, Manuel
Motivated by the Chapman Complement Theorem, we construct an isomorphism between the topological category of compact Z-sets in the Hilbert cube Q and the C0-coarse category of their complements. The C0-coarse morphisms are, in this particular case, intrinsically related to uniformly continuous proper maps. Using that fact we are able to relate in a natural way some of the topological invariants of Z-sets to the geometry of their complements.
Bounded distortion homeomorphisms on ultrametric spaces
(Annales academiae scientiarum fennicae-mathematica, 2010) Hughes, Bruce; Martínez Pérez, Álvaro; Alonso Morón, Manuel
It is well-known that quasi-isometrics between R-trees induce power quasi-symmetric homeomorphisms between their ultrametric end spaces. This paper investigates power quasi-symmetric homeomorphisms between bounded, complete, uniformly perfect, ultrametric spaces (i.e., those ultrametric spaces arising up to similarity as the end spaces of bushy trees). A bounded distortion property is found that characterizes power quasi-symmetric homeomorphisms between such ultrametric spaces that are also pseudo-doubling. Moreover, examples are given showing the extent to which the power quasi-symmetry of homeomorphisms is not captured by the quasiconformal and bi-Holder conditions for this class of ultrametric spaces.
Characteristic Curves and the exponentiation in the Riordan Lie group: A connection through examples
(2022) Chocano Feito, Pedro José; Luzón, Ana; Alonso Morón, Manuel; Prieto Martínez, Luis Felipe
We point out how to use the classical characteristic method, that is used to solve quasilinear PDE's, to obtain the matrix exponential of some lower triangle infinite matrices. We use the Lie Frechet structure of the Riordan group described in [4]. After that we describe some linear dynamical systems in K[[x]] with a concrete involution being a symmetry or a time-reversal symmetry for them. We take this opportunity to assign some dynamical properties to the Pascal Triangle.