# Reynaldo Rojas-HernándezUniversidad Michoacana de San Nicolás de Hidalgo | UMSNH

Reynaldo Rojas-Hernández

## About

23

Publications

972

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

92

Citations

Introduction

Reynaldo Rojas-Hernández currently works at the School of Science, Universidad Nacional Autónoma de México. Reynaldo does research in Geometry and Topology. Their most recent publication is 'Every Σ s -product of K -analytic spaces has the Lindelöf Σ-property'.

**Skills and Expertise**

## Publications

Publications (23)

We prove that, for any countably compact subspace X of a \(\Sigma \)-product of real lines, the space \(C_{\hspace{-1.111pt}p}(X)\) is uniformly \(\psi \)-separable, that is, has a uniformly dense subset of countable pseudocharacter. This result implies that \(C_{\hspace{-1.111pt}p}(K)\) is uniformly \(\psi \)-separable whenever K is a Valdivia com...

A set Y⊂Cp(X) is uniformly dense in Cp(X) if it is dense in the uniform topology on C(X). We construct a zero-dimensional σ-compact space X such that Cp(X) has a uniformly dense Lindelöf subspace while Cp(X) is not normal. This example answers several published open questions. Additionally, we obtain a version of a theorem of Reznichenko on ω-monol...

We provide simple characterizations of spaces admitting full r-skeletons, c-skeletons and q-skeletons, by using ω-monotone functions. We use this characterizations to prove that every countably compact space admitting a full r-skeleton is proximal; furthermore the characterizations are used to show that the class of spaces admitting full c-skeleton...

In this paper, we shall consider the hyperspace of all nontrivial convergent sequences Sc(X) of a Fréchet-Urysohn nondiscrete space X, which is equipped with the Vietoris topology. We study the spaces X for which Sc(X) is Baire: this kind of spaces have a dense subset of isolated points (see [12]). We characterize the spaces X for which Sc(X) is Ba...

Un espacio topológico X es C-normal si existe una función biyectiva f : X → Y , para algún espacio normal Y , tal que la restricción f ↾C : C → f(C) es un homeomorfismo para cada compacto C ⊂ X. El propósito de este trabajo es extender las clases conocidas de los espacios C-normales y aclarar el comportamiento de C-normalidad bajo varias operacione...

We provide an example to show that the monotone Sokolov property is not necessarily preserved under compact continuous images. Furthermore, we prove that if X ² ∖Δ X is either monotonically Sokolov or monotonically retractable, then X must be cosmic; and that if X is either hereditarily monotonically Sokolov or hereditarily monotonically retractabl...

A space Z is weakly pseudocompact if Z is Gδ-dense in at least one of its compactifications. In 1996 F.W. Eckertson [3] proposed the following problem: Find examples of Baire non Lindelöf spaces which are not weakly pseudocompact. Eckertson proposed a list of natural candidates. In this article we show that part of this list produces examples of th...

Given compact spaces X and Y, if X is Eberlein compact and Cp,n(X) is homeomorphic to Cp,n(Y) for some natural n, then Y is also Eberlein compact; this result answers a question posed by Tkachuk. Assuming existence of a Souslin line, we give an example of a Corson compact space with a Lindelöf subspace that fails to be Lindelöf Σ; this gives a cons...

In this paper we improve several results presented in [7] and in [9] related to the characterization of several kinds of pseudocompleteness and compactness properties in spaces of continuous functions of the form Cp(X,Y). In particular, we prove that for every Tychonoff space X and every separable metrizable topological group G for which Cp(X,G) is...

In this paper, we shall study categorial properties of the hyperspace of all nontrivial convergent sequences $\mathcal{S}_c(X)$ of a Fre\'ech-Urysohn space $X$, this hyperspace is equipped with the Vietoris topology. We mainly prove that $\mathcal{S}_c(X)$ is meager whenever $X$ is a crowded space, as a corollary we obtain that if $\mathcal{S}_c(X)...

We give a new characterization of Valdivia compact spaces: A compact space is Valdivia if and only if it has a dense commutatively monotonically retractable subspace. This result solves Problem 5.12 from \cite{sal-rey}. Besides, we introduce the notion of full $c$-skeleton and prove that a compact space is Corson if and only if it has a full $c$-sk...

A space X is weakly pseudocompact if it is Gδ-dense in at least one of its compactifications. X has property DY if for every countable discrete and closed subset N of X, every function f:N→Y can be continuously extended to a function over all of X. O-pseudocompleteness is the pseudocompleteness property defined by J.C. Oxtoby [17], and T-pseudocomp...

This paper is a continuation of the work done in \cite{sal-yas} and
\cite{may-pat-rob}. We deal with the Vietoris hyperspace of all nontrivial
convergent sequences $\mathcal{S}_c(X)$ of a space $X$. We answer some
questions in \cite{sal-yas} and generalize several results in
\cite{may-pat-rob}. We prove that: The connectedness of $X$ implies the
co...

In this article, we mainly study certain families of continuous retractions
($r$-skeletons) having certain rich properties. By using monotonically
retractable spaces we solve a question posed by R. Z. Buzyakova in \cite{buz}
concerning the Alexandroff duplicate of a space. Certainly, it is shown that if
the space $X$ has a full $r$-skeleton, then i...

In the set of compactifications of X we consider the partial pre-order defined by (W, h) ≤X (Z, g) if there is a continuous function f : Z ⇢ W, such that (f ∘ g)(x) = h(x) for every x ∈ X. Two elements (W, h) and (Z, g) of K(X) are equivalent, (W, h) ≡X (Z, g), if there is a homeomorphism h : W ! Z such that (f ∘ g)(x) = h(x) for every x ∈ X. We de...

We show that any ∑s-product of at most c-many L∑(≤ ω)-spaces has the L∑(≤ ω)property. This result generalizes some known results about L∑(≤ ω)spaces. On the other hand, we prove that every ∑s-product of monotonically monolithic spaces is monotonically monolithic, and in a similar form, we show that every ∑s-product of Collins-Roscoe spaces has the...

In this paper we deal with some classes of spaces defined by networks and retractions, in particular we prove: Any closed subspace in a Σ-product of cosmic spaces is monotonically stable. A space X is monotonically retractable if and only if it is monotonically ω-stable and has a full retractional skeleton. Any monotonically retractable and monoton...

We introduce the monotone Sokolov property and show that it is dual to monotone retractability in the sense that X is monotonically retractable if and only if Cp(X)Cp(X) is monotonically Sokolov. Besides, a space X is monotonically Sokolov if and only if Cp(X)Cp(X) is monotonically retractable. Monotone retractability and monotone Sokolov property...

The notion of monotonically monolithic space was introduced by V.V. Tkachuk in 2009 [8]. In this paper we introduce the notion of monotone stability and show that a space Cp(X)Cp(X) is monotonically monolithic if and only if X is monotonically stable. As a consequence, a space Cp(X)Cp(X) is monotonically stable if and only if X is monotonically mon...

Let CL(X)CL(X) and K(X)K(X) denote the hyperspaces of non-empty closed and non-empty compact subsets of X, respectively, with the Vietoris topology. In this paper we show that, given an ordinal number γ, the space K([0,γ))K([0,γ)) is C-embedded in CL([0,γ))CL([0,γ)) if and only if cof(γ)≠ωcof(γ)≠ω. Moreover we answer some problems posed by the firs...

In this article we introduce the notion of monotonically retractable space and we show that: (1) Cp(X) is Lindelöf and a D-space whenever X is monotonically retractable. (2) If X is monotonically retractable then C p,2n(X) is monotonically retractable for any n ∈ ω. (3) Any first countable countably compact subspace of an ordinal is monotonically r...

In this article we answer some questions related to monotonically monolithic spaces posed in O.T. Alas et al. (2009) [1], V.V. Tkachuk (2009) [17], and V.V. Tkachuk (2012) [18]. We prove: (1) Cp(Cp(X))Cp(Cp(X)) is monotonically monolithic if and only if X is monotonically monolithic; (2) if X is a ΣκΣκ-product of a family of spaces with countable n...