Recent papers in topology

Prof. Dr. Ljubiša D. R. Kočinac
E-Mail Website
Guest Editor

Faculty of Sciences and Mathematics, University of Niš, 18000 Niš, Serbia
Interests: general topology; mathematical analysis

Dear Colleagues,

In recent years, there has been a vast body of literature on theoretical development in topology and applications of topological methods in a wide variety of areas of mathematics and other sciences.

The aim of this Special Issue, which is devoted mainly to general topology, is to collect recent noteworthy results and original research focusing on the latest progress and developments in this research area and its applications. We hope that this Issue will provide a good platform for researchers in different areas of topology and its applications to come together and exchange ideas on how we can further develop and apply topology. Only high-quality papers will be accepted for publication.

Potential topics include, but are not limited to, the following:

• Function spaces and hyperspaces;
• Uniform spaces;
• Topological algebra;
• Cardinal invariants;
• Selection principles theory;
• Game theory in topology;
• Fuzzy topology;
• Soft and rough topological spaces;
• Digital topology;
• Fixed point theory;
• Topological methods in analysis;
• Combinatorial topology.

Prof. Dr. Ljubiša D. R. Kočinac
Guest Editor

Manuscript Submission Information

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• selection principles
• game theory in topology
• function spaces and hyperspaces
• cardinal invariants
• soft topology
• topological groups
• asymptotic analysis

Published Papers [1 paper]

• Rajish Kumar
• Sunil Jacob John
• Sovan Samanta

In this paper, we emphasize how M-topological concepts like closed sets, closure of submsets, etc., differ from similar concepts in general topology. Further, we discuss the open cover of a submset in two different subspace M-topologies and define two distinct types of compactness for a submset. Conditions in terms of counts are obtained for induci...

• Xuexing Lu
• Ziqian Tang

In this paper, we introduce a generalized topological quantum field theory based on the symmetric monoidal category which we call causal network condensation since it can be regarded as a generalization of spin network construction of Baez, Turaev-Viro model and causal set theory. In this paper we introduce some new concepts, including causal netwo...

• Bey-Chi Lin
• Chin-Tau Lea

Conventional theory for designing strictly nonblocking networks, such as crossbars or Clos networks, assumes that these networks have a centralized topology. Many new applications, however, require networks to have a distributed topology, like 2-D mesh or torus. In this paper, we present a new theoretical framework for designing such nonblocking ne...

• Samer Al-Ghour

In this paper, we introduce the class of soft semi ω-open sets of a soft topological space [X,τ,A], using soft ω-open sets. We show that the class of soft semi ω-open sets contains both the soft topology τω and the class of soft semi-open sets. Additionally, we define soft semi ω-closed sets as the class of soft complements of soft semi ω-open sets...

• Benjamin A. Burton
• Alexander He

For many fundamental problems in computational topology, such as unknot recognition and 3-sphere recognition, the existence of a polynomial-time solution remains unknown. A major algorithmic tool behind some of the best known algorithms for these problems is normal surface theory. However, we currently have a poor understanding of the computational...

• Ritu Sen

In this paper our main interest is to introduce a new type of generalized open sets defined in terms of an operation on a generalized topological space. We have studied some properties of this newly defined sets. As an application, we have introduced some weak separation axioms and discussed some of their properties. Finally, we have studied some p...

• Saharon Shelah

We prove some results in set theory as applied to general topology and model theory. In particular, we study ℵ1-collectionwise Hausdorff, Chang Conjecture for logics with Malitz-Magidor quantifiers and monadic logic of the real line by odd/even Cantor sets.

• Ismat Beg

The aim of this article is to introduce a new notion of ordered convex metric spaces and study some basic properties of these spaces. Several characterizations of these spaces are proven that allow making geometric interpretations of the new concepts. 1. Introduction Menger [1] initiated the study of convexity in metric spaces which was further de...

• Samer Al-Ghour

We define soft ωp-openness as a strong form of soft pre-openness. We prove that the class of soft ωp-open sets is closed under soft union and do not form a soft topology, in general. We prove that soft ωp-open sets which are countable are soft open sets, and we prove that soft pre-open sets which are soft ω-open sets are soft ωp-open sets. In addit...

• Federico Brunero
• Petros Elia

This work identifies the fundamental limits of Multi-Access Coded Caching [MACC] where each user is connected to multiple caches in a manner that follows a generalized combinatorial topology. This topology stands out as it allows for unprecedented coding gains, even with very modest cache resources. First, we extend the setting and the scheme prese...

• U. P. Tyagi
• Kakoli Bera
• Partha Goswami

We study surface state of a generic topological Kondo insulator [TKI] system, viz. SmB6, by performing a mean-field theoretic [MFT] calculation within the frame-work of periodic Anderson model [PAM] using slave-boson technique. The surface metallicity together with bulk insulation is found to require strong f-electron localization. A key distinctio...

• Clovis Hamel
• Franklin D. Tall

We present applications of $C_p$-theory, the branch of general topology concerned with spaces of real-valued continuous functions, to model theory, mostly in the context of continuous logics. We include $C_p$-theoretic results and proofs in a self-contained way for model theorists who are not familiar with the techniques of this field. We further g...

• Gemechu Adem

This is an introductory course in topology with metric spaces treating topics such as open sets, closed sets, continuity, convergences and completeness, and it extends the ideas to generate topological spaces and topological properties like connectedness and compactness

• Kathryn Hess
• Nima Rasekh

The theory of shadows is an axiomatic, bicategorical framework that generalizes topological Hochschild homology [THH] and satisfies analogous important properties, such as Morita invariance. Using Berman's extension of THH to bicategories, we prove that there is an equivalence between functors out of THH of a bicategory and shadows on that bicatego...

• Raja Latif

In 2016 Hakeem A. Othman and Md. Hanif Page introduced a new notion of set in general topology called an infra -α- open set and investigated its fundamental properties and studied the relationship between infra -α- open set and other topological sets. The objective of this paper is to introduce the new concepts called infra -α- compact space, count...

• Colin David Reid

Motivated by the problem of finding a "well-foundedness principle" for totally disconnected, locally compact [t.d.l.c.] groups, we introduce a class $\mathscr{E}^{\mathscr{S}}$ of t.d.l.c. groups, containing P. Wesolek's class $\mathscr{E}$ of [regionally] elementary groups but also including many groups in the class $\mathscr{S}$ of nondiscrete co...

• Mohammad Shawqi Sarsak

Sarsak [On μ\mu -compact sets in μ\mu -spaces, Questions Answers Gen. Topology 31 [2013], no. 1, 49–57] introduced and studied the class of μ\mu -Lindelöf sets in μ\mu -spaces. Mustafa [μ\mu -semi compactness and μ\mu -semi Lindelöfness in generalized topological spaces, Int. J. Pure Appl. Math. 78 [2012], no. 4, 535–541] introduced and studied...

• Nadia Gheith
• Samirah ALZahrani

A topological space is called epi--normal [epi--normal] if there is a coarser topology on such that is -normal [-normal]. We investigate these properties and show some examples to explain the relationships of epi--normal [epi--normal] with other weaker versions of normality and some topological spaces. 1. Introduction In [1], the notions of -norma...

• Milan Matejdes

The article deals with the correspondence between soft ideal topological spaces and ideal topological ones. Investigation of soft ideal topological spaces is based on methods of general topology and the application of results for soft omega open and strongly soft omega open sets is given.

• Samer Al-Ghour

Soft ωs-open sets as a class of soft sets that lies strictly between soft open sets and soft semi-open sets is introduced. The natural properties of soft ωs-open sets are described. Using soft ωs-open sets, soft ωs-closure and soft ωs-interior as new soft operators are defined and investigated. Furthermore, the relationships regarding generated sof...

• Andras Blazsek

∂ Topological Landscapes [2015–ongoing] is a multisensory environment that comprises three projects, all based on research into the controversial healing instruments designed by Southern California inventor Royal Raymond Rife [Nebraska, 1888–California, 1971]. Rife’s early twentieth-century scientific work involved light microscopy, frequency theor...

• Abdelwaheb Mhemdi
• Tareq Al-shami

In this paper, we define a new family of separation axioms in the classical topology called functionally Ti spaces for i=0,1,2. With the assistant of illustrative examples, we reveal the relationships between them as well as their relationship with Ti spaces for i=0,1,2. We demonstrate that functionally Ti spaces are preserved under product spaces,...

• Jianjie Li
• Yuqi Gao
• Xuan Yu

Background The hypoxia-inducible factor-1 [HIF-1] signaling pathway is an important topic in high-altitude medicine. Network analysis is a novel method for integrating information on different aspects and levels of biological networks. However, this method has not been used in research on the HIF-1 signaling pathway network. To introduce this metho...

• William J. Torres Bobadilla

A bstract The causal representation of multi-loop scattering amplitudes, obtained from the application of the loop-tree duality formalism, comprehensively elucidates, at integrand level, the behaviour of only physical singularities. This representation is found to manifest compact expressions for multi-loop topologies that have the same number of v...

• Tareq Al-shami
• El-Sayed Abo-Tabl

Soft set theory is a theme of interest for many authors working in various areas because of its rich potential for applications in many directions. it received the attention of the topologists who always seeking to generalize and apply the topological notions on different structures. To contribute to this research area, in this paper, we formulate...

• Svetlana V. Butler

This paper is one in a series that investigates topological measures on locally compact spaces. A topological measure is a set function which is finitely additive on the collection of open and compact sets, inner regular on open sets, and outer regular on closed sets. We examine semisolid sets and give a way of constructing topological measures fro...

• Yu-Lin Chou

The concept of a limit point of a sequence is arguably a ``blind spot'' in the related introductory teaching materials in contrast with the other concepts mentioned in the title that usually get a clear definitive treatment. We provide without loss of rigor an accessible treatment of limit point adapted from the existing literature of general topo...

• Jacek Hejduk
• Eliza Wajch

A strong generalized topological space is an ordered pair $\mathbf{X}=\langle X, \mathcal{T}\rangle$ such that $X$ is a set and $\mathcal{T}$ is a collection of subsets of $X$ such that $\emptyset, X\in \mathcal{T}$ and $\mathcal{T}$ is stable under arbitrary unions. A necessary and sufficient condition for a strong generalized topological space $\...

• I. Brunner
• I. Mayer
• C. Schmidt-Colinet

A bstract We study the effect of bulk perturbations of N=[2] superconformal minimal models on topological defects. In particular, symmetries and more general topological defects which survive the flow to the IR are identified. Our method is to consider the topological subsector and make use of the Landau-Ginzburg formulation to describe RG flows an...