Applied General Topology

Let X be a smooth fan and denote its set of endpoints by E(X). Let E be one of the following spaces: the natural numbers, the irrational numbers, or the product of the Cantor set with the natural numbers. We prove that there is a smooth fan X such that E(X) is homeomorphic to E and for every homeomorphism h : X → X , the restriction of h to E(X) is the identity. On the other hand, we also prove that if X is any smooth fan such that E(X) is homeomorphic to complete Erdős space, then X is necessarily homeomorphic to the Lelek fan; this adds to a 1989 result by Włodzimierz Charatonik.

Rodrigo Hernández-Gutiérrez

Logan C. Hoehn

Smooth fans that are endpoint rigid

端点刚性的光滑扇形

In this note, we show that the main result (Theorem 3.2) due to Asim et al. (Appl. Gen. Topol., 23(2), 363-376 (2022) https://doi.org/10.4995/agt.2022.17418) is still valid if we remove the assumption of continuity of the mapping.

Mujahid Abbas

Rizwan Anjum

Rabia Anwar

A note on the fixed point theorem of F-contraction mappings in rectangular M-metric space

关于矩形M-度量空间中F-压缩映射的不动点定理的注记

We answer questions of Arhangel'skiĭ using spaces defined from combinatorial objects. We first establish further convergence properties of a space constructed from □ ( κ ) showing it is Fréchet-Urysohn for finite sets and a w-space that is not a W-space. We also show that under additional assumptions it may be not bi-sequential, and so providing a consistent example of an absolutely Fréchet α1 space that is not bisequential. In addition, if we do not require the space being α1, we can construct a ZFC example of a countable absolutely Fréchet space that is not bisequential from an almost disjoint family of subsets of the natural numbers.

William Chen-Mertens

César Corral-Rojas

Paul J. Szeptycki

Strong Fréchet properties of spaces constructed from squares and AD families

由平方和AD族构造的空间的强Fréchet性质

This paper continues a series discussing flaws in published assertions concerning fixed points in digital metric spaces.

Laurence Boxer

Remarks on fixed point assertions in digital topology, 6

关于数字拓扑中不动点断言的评述，6

In this paper, we prove the existence of fixed point results for set-valued mappings in Menger probabilistic metric spaces equipped with an amorphous binary relation and a Hadžić -type t-norm. For the usability of such findings we present a Kelisky-Rivlin type result for a class of Bernstein type special operators introduced by Deo et. al. [Appl. Math. Comput. 201, (2008), 604-612 ] on the space C([ 0, n/n+1]). In this way, these investigations extend, modify and generalize some prominent recent fixed point results of the existing literature.

Gopi Prasad

Sheetal Deshwal

Rupesh K. Srivastav

Fixed points of set-valued mappings in Menger probabilistic metric spaces endowed with an amorphous binary relation

Menger概率度量空间中具有不定二元关系的集值映射的不动点

Given a metric continuum X, we consider the collection of all regular subcontinua of X and the collection of all meager subcontinua of X, these hyperspaces are denoted by D(X) and M(X), respectively. It is known that D(X) is compact if and only if D(X) is finite.In this way, we find some conditions related about the cardinality of D(X) and we reduce the fact to count the elements of D(X) to a Graph Theory problem, as an application of this, we prove in particular that | D ( X ) | ∉ { 2,3,4,5,8 , 9 } h t ) for any continuum X. Also, we prove that D(X) is never homeomorphic to ℕ . On the other hand, given a point p ∈ X , we consider the meager composant and the filament composant of p in X, denoted by MXp and FcsX(p), respectively, and we study some relations between MXp and FcsX(p) such as the equality of them as a subset of X. Also, we construct examples showing that the collection Fcs ( X ) = { FcsX ( p ) : p ∈ X } can be homeomorphic to: any finite discrete space, the harmonic sequence, the closure of the harmonic sequence and the Cantor set. Finally, we study the contractibility of M(X); we prove the arc of pseudo-arcs, which is a no contractible continuum, satisfies that its hyperspace of meager subcontinua is contractible, given a solution to an open problem. Also, we rise open problems.

Javier Camargo

Norberto Ordoñez

Diego Ramírez

On the hyperspaces of meager and regular continua

关于贫集和正则连续统的超空间

The aim of this paper is to study some variants of nowhere dense sublocales called maximal nowhere dense and homogeneous maximal nowhere dense sublocales. These concepts were initially introduced by Veksler in classical topology. We give some general properties of these sublocales and further examine their relationship with both inaccessible sublocales and remote sublocales. It turns out that a locale has all of its non-void nowhere dense sublocales maximal nowhere dense precisely when all of its its non-void nowhere dense sublocales are inaccessible. We show that the Booleanization of a locale is inaccessible with respect to every dense and open sublocale. In connection to remote sublocales, we prove that, if the supplement of an open dense sublocale S is homogeneous maximal nowhere dense, then every S#-remote sublocale is *-remote from S. Every open localic map that sends dense elements to dense elements preserves and reflects maximal nowhere dense sublocales. If such a localic map is further injective, then it sends homogeneous maximal nowhere dense sublocales back and forth.

Mbekezeli Nxumalo

On maximal nowhere dense sublocales

关于极大无处稠密子局部

In this note, we introduce and study the concept of a semi-strongly irreducible ideal, a natural generalization of a strongly irreducible ideal. We say an ideal I of a commutative ring R is semi-strongly irreducible if for ideals J and K of R, the inclusion J ∩ K ⊆ I implies that either J2 ⊆ I or K2 ⊆ I . After some general results, the article focuses on semi-strongly irreducible ideals in rings of continuous functions.

Jamal Hashemi

Hossein Yari

A generalization of strongly irreducible ideals with a view towards rings of continuous functions

强不可约理想的推广及其在连续函数环中的应用

In this paper we provide some general results about topological spaces X which satisfy starn- P , weakly starn- P and almost starn- P, for P∈ { κ ᴄᴄ , W κ L , ᴅ κ ᴄᴄ } , where κ is an infinite cardinal number. The particular cases when κ = ω , P ∈ { ᴄᴄᴄ , weakly Lindelöf , ᴅ ᴄᴄᴄ } are obtained. Furthermore, for the same classes of spaces defined by such P, by applying Erdős-Radó's theorem and using the rank l-diagonal notion, we establish some cardinal inequalities.

Ricardo Cruz-Castillo

Alejandro Ramírez-Páramo

Jesús F. Tenorio

Some results on weaker forms of starn-CCC, weakly Lindelöf and starn-DCCC spaces

关于starn-CCC、弱Lindelöf和starn-DCCC空间的一些较弱形式的结果

We present a comprehensive report on the relationships between variations of the Menger and Rothberger selection properties with respect to w-covers and k-covers in the most general topological setting and address the finite productivity of some of these properties. We collect various examples that separate certain properties and we carefully identify which separation axioms simplify aspects of these properties. We finish with a consolidated list of open questions focused on topological examples.

短名	Appl. Gen. Topol.
Journal Impact	0.80
国际分区	MATHEMATICS(Q3)

ISSN	1576-9402, 1989-4147
h-index	15

涉及主题	topological dynamicstopological algebrahyperspaces
出版信息	出版商: Universidad Politecnica de Valencia，出版周期: ，期刊类型: journal，开源期刊: 是
基本数据	创刊年份: 2007，原创研究文献占比: ，自引率:， Gold OA占比:
平均审稿周期	15 weeks

Applied General Topology

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