Papers by Alejandro Illanes
Virtual Special Issue – The Mexican International Conference on Topology and Its Applications (MICTA-2014)Preface
Topology and its Applications, 2017
arXiv (Cornell University), Dec 19, 2022
A metric continuum X is indecomposable if it cannot be put as the union of two of its proper subc... more A metric continuum X is indecomposable if it cannot be put as the union of two of its proper subcontinua. A subset R of X is said to be continuumwise connected provided that for each pair of points p, q ∈ R, there exists a subcontinuum M of X such that {p, q} ⊂ M ⊂ R. Let X 2 denote the Cartesian square of X and ∆ the diagonal of X 2. In [7] it was asked if for a continuum X, distinct from the arc, X 2 \ ∆ is continuumwise connected if and only if X is decomposable. In this paper we show that no implication in this question holds. For the proof of the non-necessity, we use the dynamic properties of a suitable homeomorphism of the Cantor set onto itself to construct an appropriate indecomposable continuum X.
Hyperspace of arcs and singletons of a continuum
33rd Summer Conference on Topology and its Applications, 2018
The Work of Sam B. Nadler, Jr. on Hyperspaces
Continuum Theory, 2002
Jounal of Negative and No Positive Results, 2020
Introducción. Los escolares, más concretamente en secundaria, se encuentran en un momento crucial... more Introducción. Los escolares, más concretamente en secundaria, se encuentran en un momento crucial para la adquisición de diferentes hábitos que marcarán su estilo de vida y su evolución en la edad adulta. La cultura deportiva, valorar la relevancia del ejercicio físico y conocer cuáles son las ventajas de una vida saludable, son factores que debemos potenciar como docentes. Actualmente, la literatura científica evidencia la relevancia de la práctica de actividad física y su influencia en la mejora del rendimiento académico de los estudiantes. Objetivos. Conocer qué tipo de intensidad y ejercicio físico mejora los procesos cognitivos. Revisar cuál es el motivo de la mejora del rendimiento académico. Método. Se analizaron diversas bases de datos entre las que destacan Pubmed, Scielo, Dialnet y Google Académico, escogiendo un total de 72 artículos en la primera selección, utilizándose finalmente un total de 20. Resultados y conclusiones. Se aprecia una relación directa lineal y positiv...
arXiv (Cornell University), Dec 6, 2018
Given a collection of pairwise co-prime integers m1,. .. , mr, greater than 1, we consider the pr... more Given a collection of pairwise co-prime integers m1,. .. , mr, greater than 1, we consider the product Σ = Σm 1 × • • • × Σm r , where each Σm i is the mi-adic solenoid. Answering a question of D. P. Bellamy and J. M. Lysko, in this paper we prove that if M is a subcontinuum of Σ such that the projections of M on each Σm i are onto, then for each open subset U in Σ with M ⊂ U , there exists an open connected subset V of Σ such that M ⊂ V ⊂ U ; i.e. any such M is ample in the sense of Prajs and Whittington [10]. This contrasts with the property of Cartesian squares of fixed solenoids Σm i × Σm i , whose diagonals are never ample [1].
Commentationes Mathematicae Universitatis Carolinae, 2012
Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digi... more Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.
Topology and its Applications, Jun 1, 2016
Abstract Let X be a metric continuum and C ( X ) the hyperspace of subcontinua of X . A Whitney b... more Abstract Let X be a metric continuum and C ( X ) the hyperspace of subcontinua of X . A Whitney block is a set of the form μ − 1 ( [ s , t ] ) , where μ : C ( X ) → [ 0 , 1 ] is a Whitney map and 0 ≤ s t 1 . In this paper we study continua for which Whitney blocks are homeomorphic to X × [ 0 , 1 ] . We characterize an arc, a simple closed curve and simple n -ods in terms of Whitney blocks. We also show that if X is arc-like, then each Whitney block for C ( X ) is 2-cell-like; and if X is circle-like, then each Whitney block of the form μ − 1 ( [ 0 , t ] ) is ring-like.
Homogeneity Degree of Hyperspaces of Arcs and Simple Closed Curves
Rocky Mountain Journal of Mathematics, Apr 1, 2023
Problems on hyperspaces of continua, some answers
Topology and its Applications, Apr 1, 2022
M-confluent maps, an example
Boletin De La Sociedad Matematica Mexicana, 1997
For each n > 3, we construct hereditarily decomposable continua X and Y and a map f:X —>Y s... more For each n > 3, we construct hereditarily decomposable continua X and Y and a map f:X —>Y such that Y does not contain n-ods and f is not (2ra — 5)confluent, i.e., there exists a subcontinuum M of Y such that M is not the image of 2n ~ 5 components of f"1(M). This answers a question by E.E. Grace and E.J. Vought.
Topology and its Applications, 2009
Let Y be a metric continuum. Let C n (Y) be the hyperspace of nonempty closed subsets of Y with a... more Let Y be a metric continuum. Let C n (Y) be the hyperspace of nonempty closed subsets of Y with at most n components. In this paper we show that if X is a dendrite with closed set of end points and C 2 (X) is homeomorphic to C 2 (Y), for some dendrite Y , then X is homeomorphic to Y. This completes the work by David Herrera-Carrasco and Fernando Macías-Romero who previously proved the corresponding result for each n = 2.
Cells in $n$-fold hyperspaces
Colloquium Mathematicum, 2018
arXiv (Cornell University), Dec 14, 2022
Given a metric continuum X, a nonempty proper closed subspace B of X, does not block a point p ∈ ... more Given a metric continuum X, a nonempty proper closed subspace B of X, does not block a point p ∈ X \B provided that the union of all subcontinua of X containing p and contained in X \B is a dense subset of X. The collection of all nonempty proper closed subspaces B of X such that B does not block any element of X \B is denoted by N B(F 1 (X)). In this paper we prove that for each completely metrizable and separable space Z, there exists a continuum X such that Z is homeomorphic to N B(F 1 (X)). This answers a series of questions by Camargo, Capulín, Castaneda-Alvarado and Maya.
Acta Mathematica Hungarica, Dec 13, 2015
Let X and Y be metric continua. We consider the following property (*) if M is a subcontinuum of ... more Let X and Y be metric continua. We consider the following property (*) if M is a subcontinuum of X × Y such that π X (M) = X and π Y (M) = Y , where πX and πY are the respective projections on X and Y , then M has small open connected neighborhoods in X × Y. Answering questions by D. P. Bellamy and J. M. � Lysko, we prove that (a) the product of the pseudoarc and any Knaster continuum has property (*), and (b) there exist chainable indecomposable continua X and Y such that X × Y does not have property (*).
arXiv (Cornell University), Jun 24, 1999
An example is given of a compact absolute retract that is not a Hilbert cube manifold but whose s... more An example is given of a compact absolute retract that is not a Hilbert cube manifold but whose second symmetric porduct is the Hilbert cube. A factor theorem is given for nth symmetric product of the cartesian product of any absolute neighborhood retract with the Hilbert cube. A short proof is included of the known fact that symmetric products preserve the property of being a compact Hilbert cube manifold (the theorem is proved here for all Hilbert cube manifolds).
Applied general topology, Oct 3, 2022
Let X be a metric continuum and n ∈ N. Let Fn(X) be the hyperspace of nonempty subsets of X with ... more Let X be a metric continuum and n ∈ N. Let Fn(X) be the hyperspace of nonempty subsets of X with at most n points. If 1 ≤ m < n, we consider the quotient space F n m (X) = Fn(X)/Fm(X). Given a mapping f : X → X, we consider the induced mappings fn : Fn(X) → Fn(X) and f n m : F n m (X) → F n m (X). In this paper we study relations among the dynamics of the mappings f , fn and f n m and we answer some questions, by F. Barragán, A. Santiago-Santos and J. Tenorio, related to the properties: minimality, irreducibility, strong transitivity and turbulence.
summary:Conditions are investigated that imply noncontractibility of curves. In particular, a pla... more summary:Conditions are investigated that imply noncontractibility of curves. In particular, a plane noncontractible dendroid is constructed which contains no homotopically fixed subset. A new concept of a homotopically steady subset of a space is introduced and its connections with other related concepts are studied
Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digi... more Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.
Topology and its Applications, 2017
We characterize chainable continua X for which the diagonal Δ in X × X has small connected neighb... more We characterize chainable continua X for which the diagonal Δ in X × X has small connected neighborhoods. That means that for each open subset W of X × X with Δ ⊂ W , there exists a connected subset M of X × X such that Δ ⊂ int X×X (M) ⊂ M ⊂ W .
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Papers by Alejandro Illanes