The metric confluent images of half-lines and lines
The monad induced by the hom-functor in the category of topological spaces and its associated Eilenberg-Moore algebras.
The monomorphism semigroup of S(X).
The Nachbin compactification via convergence ordered spaces.
The nonexistence of expansive homeomorphisms of chainable continua
A homeomorphism f:X → X of a compactum X with metric d is expansive if there is c > 0 such that if x, y ∈ X and x ≠ y, then there is an integer n ∈ ℤ such that . In this paper, we prove that if a homeomorphism f:X → X of a continuum X can be lifted to an onto map h:P → P of the pseudo-arc P, then f is not expansive. As a corollary, we prove that there are no expansive homeomorphisms on chainable continua. This is an affirmative answer to one of Williams’ conjectures.
The nonexistence of expansive homeomorphisms of dendroids
The one-point countable compactification of curve spaces and arc spaces
The order topology for function lattices and realcompactness.
The origins of the concept of dimension
The partially ordered collection of regular ...-classes of S(X).
The Peano curves as limit of α-dense curves.
En este artículo presentamos una caracterización de las curvas de Peano como límite uniforme de sucesiones de curvas α-densas en el compacto que es llenado por la curva de Peano. Estas curvas α-densas deben tener densidades tendiendo a cero y sus funciones coordenadas deben de ser de variación tendiendo a infinito cuando α tiende a cero.
The product of two ordinals is hereditarily dually discrete
In Dually discrete spaces, Topology Appl. 155 (2008), 1420–1425, Alas et. al. proved that ordinals are hereditarily dually discrete and asked whether the product of two ordinals has the same property. In Products of certain dually discrete spaces, Topology Appl. 156 (2009), 2832–2837, Peng proved a number of partial results and left open the question of whether the product of two stationary subsets of is dually discrete. We answer the first question affirmatively and as a consequence also give...
The pseudo-arc as an inverse limit with simple bonding maps
The rank of the diagonal and submetrizability
Several topological properties lying between the submetrizability and the -diagonal property are studied. We are mostly interested in their relationship to each other and to the submetrizability. The first example of a Tychonoff space with a regular -diagonal but without a zero-set diagonal is given. The same example shows that a Tychonoff separable space with a regular -diagonal need not be submetrizable. We give a necessary and sufficient condition for submetrizability of a regular separable...
The realization of dimension function
The set function T and homotopies
The set functions 𝓣 and 𝒦 and irreducible continua
We study the set functions 𝓣 and 𝒦 on irreducible continua. We present several properties of these functions when defined on irreducible continua. In particular, we characterize the class of irreducible continua for which these functions are continuous. We also characterize the class of 𝒦-symmetric irreducible continua.
The shrinking property and the B-property in ordered spaces
The solenoids are the only circle-like continua that admit expansive homeomorphisms
A homeomorphism h:X → X of a compactum X is expansive provided that for some fixed c > 0 and any distinct x, y ∈ X there exists an integer n, dependent only on x and y, such that d(hⁿ(x),hⁿ(y)) > c. It is shown that if X is a circle-like continuum that admits an expansive homeomorphism, then X is homeomorphic to a solenoid.
The Sorgenfrey line has no connected compactification