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Mathematics
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Topological Space and Its Applications
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Topological Space and Its Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Algebra, Geometry and Topology".

Deadline for manuscript submissions: closed (31 March 2024) | Viewed by 8573

Special Issue Editors

Dr. Lakshmi Kanta Dey

E-Mail Website
Guest Editor
Department of Mathematics, National Institute of Technology Durgapur, Durgapur 713209, West Bengal, India
Interests: topology; coding and design theory; functional analysis; fixed point theory; nonlinear analysis
Prof. Dr. Pratulananda Das

E-Mail Website
Guest Editor
Department of Mathematics, Jadavpur University, Kolkata 700032, India
Interests: topology; set theory; set theoretic and general topology; analysis; sequences and summability theory

Special Issue Information

Dear Colleagues,

General topology, topological spaces, and analysis compose a crucial mathematical branch not only for its immense potential to develop its own disciplinary body but also mostly due to its basic nature, for its ability to interact and applicability in other fields of both mathematics and other relevant scientific areas. Certainly, the research on topology includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interaction between topology and other mathematical disciplines, e.g., topological algebra, topological dynamics, functional analysis, and category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research on topology. In addition, fixed-point theory itself is a beautiful mixture of analysis (pure and applied), topology and geometry. Many situations in the study of nonlinear equations, calculus of variations, partial differential equations, optimal control and inverse problems can be formulated in terms of fixed-point problems or optimization.

The main purpose of this Special Issue, which is by and large committed to the broad area of topological spaces, is to collect recent noteworthy results and original research focusing on the latest progress and developments in this research area and its applications. Some well-written expository articles on recent advances could also be considered. We hope that this Special 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 the basic topics that are theoretical in nature as well as on new applications of topology.

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

  • Topological vector spaces;
  • Function spaces and hyperspaces;
  • Set theoretic topology;
  • Topological dynamics;
  • Continuum theory;
  • Topological algebra;
  • Category theory;
  • Soft and rough topological spaces;
  • Applications to differential equations and dynamical systems;
  • Fixed point theory;
  • Topological methods in nonlinear analysis.

Dr. Lakshmi Kanta Dey
Prof. Dr. Pratulananda Das
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • topological space
  • topological dynamics
  • topological algebra
  • fractal manifold
  • fractal topology
  • Borsuk–Ulam-type results
  • fixed point

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Further information on MDPI's Special Issue polices can be found here.

Published Papers (7 papers)

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Research

13 pages, 270 KiB  
Article
On the Injectivity of Euler Integral Transforms with Hyperplanes and Quadric Hypersurfaces
by Mattie Ji
Mathematics 2024, 12(15), 2339; https://doi.org/10.3390/math12152339 - 26 Jul 2024
Viewed by 511
Abstract
The Euler characteristic transform (ECT) is an integral transform used widely in topological data analysis. Previous efforts by Curry et al. and Ghrist et al. have independently shown that the ECT is injective on all compact definable sets. In this work, we first [...] Read more.
The Euler characteristic transform (ECT) is an integral transform used widely in topological data analysis. Previous efforts by Curry et al. and Ghrist et al. have independently shown that the ECT is injective on all compact definable sets. In this work, we first study the injectivity of the ECT on definable sets that are not necessarily compact and prove a complete classification of constructible functions that the Euler characteristic transform is not injective on. We then introduce the quadric Euler characteristic transform (QECT) as a natural generalization of the ECT by detecting definable shapes with quadric hypersurfaces rather than hyperplanes. We also discuss some criteria for the injectivity of QECT. Full article
(This article belongs to the Special Issue Topological Space and Its Applications)
16 pages, 318 KiB  
Article
Barrelled Weakly Köthe–Orlicz Summable Sequence Spaces
by Issam Aboutaib, Janusz Brzdęk and Lahbib Oubbi
Mathematics 2024, 12(1), 88; https://doi.org/10.3390/math12010088 - 26 Dec 2023
Viewed by 823
Abstract
Let E be a Hausdorff locally convex space. We investigate the space Λφ[E] of weakly Köthe–Orlicz summable sequences in E with respect to an Orlicz function φ and a perfect sequence space Λ. We endow [...] Read more.
Let E be a Hausdorff locally convex space. We investigate the space Λφ[E] of weakly Köthe–Orlicz summable sequences in E with respect to an Orlicz function φ and a perfect sequence space Λ. We endow Λφ[E] with a Hausdorff locally convex topology and determine the continuous dual of the so-obtained space in terms of strongly Köthe–Orlicz summable sequences from the dual space E′ of E. Next, we give necessary and sufficient conditions for Λφ[E] to be barrelled or quasi-barrelled. This contributes to the understanding of different spaces of vector-valued sequences and their topological properties. Full article
(This article belongs to the Special Issue Topological Space and Its Applications)
13 pages, 296 KiB  
Article
Primal Structure with Closure Operators and Their Applications
by Ahmad Al-Omari and Mesfer H. Alqahtani
Mathematics 2023, 11(24), 4946; https://doi.org/10.3390/math11244946 - 13 Dec 2023
Cited by 5 | Viewed by 1045
Abstract
Acharjee et al. have created a new structure in mathematics called a primal. Therefore, the primary goal of this research was to introduce and explore more primal space features. Additionally, we studied some of the fundamental characteristics of two novel operators that we [...] Read more.
Acharjee et al. have created a new structure in mathematics called a primal. Therefore, the primary goal of this research was to introduce and explore more primal space features. Additionally, we studied some of the fundamental characteristics of two novel operators that we define using primal spaces. Using these new operators, we were able to create a weaker version of the original topology. Finally, we provide some examples to further illustrate our discussion of some of their characteristics. Full article
(This article belongs to the Special Issue Topological Space and Its Applications)
8 pages, 255 KiB  
Article
Quasihomeomorphisms and Some Topological Properties
by Khedidja Dourari, Alaa M. Abd El-latif, Sami Lazaar, Abdelwaheb Mhemdi and Tareq M. Al-shami
Mathematics 2023, 11(23), 4748; https://doi.org/10.3390/math11234748 - 24 Nov 2023
Viewed by 912
Abstract
In this paper, we study the properties of topological spaces preserved by quasihomeomorphisms. Particularly, we show that quasihomeomorphisms preserve Whyburn, weakly Whyburn, submaximal and door properties. Moreover, we offer necessary conditions on continuous map q:X→Y where Y is Whyburn [...] Read more.
In this paper, we study the properties of topological spaces preserved by quasihomeomorphisms. Particularly, we show that quasihomeomorphisms preserve Whyburn, weakly Whyburn, submaximal and door properties. Moreover, we offer necessary conditions on continuous map q:X→Y where Y is Whyburn (resp., weakly Whyburn ) in order to render X Whyburn (resp., weakly Whyburn). Also, we prove that if q:X→Y is a one-to-one continuous map and Y is submaximal (resp., door), then X is submaximal (resp., door). Finally, we close this paper by studying the relation between quasihomeomorphisms and k-primal spaces. Full article
(This article belongs to the Special Issue Topological Space and Its Applications)
10 pages, 302 KiB  
Article
A Novel Class of Separation Axioms, Compactness, and Continuity via C-Open Sets
by Mesfer H. Alqahtani and Hind Y. Saleh
Mathematics 2023, 11(23), 4729; https://doi.org/10.3390/math11234729 - 22 Nov 2023
Cited by 2 | Viewed by 848
Abstract
In this paper, we originate a new class of open sets, namely C-open sets, and we review its important properties. Then, some separation axioms of C-open sets are introduced and investigated. In addition, we define the so-called C-compact and [...] Read more.
In this paper, we originate a new class of open sets, namely C-open sets, and we review its important properties. Then, some separation axioms of C-open sets are introduced and investigated. In addition, we define the so-called C-compact and C′-compact spaces via C-open sets, and the theorems based on them are discussed with counterexamples. Moreover, we entitle the C-continuous and C′-continuous functions by applying C-open sets. In particular, several inferred properties of them and their connection with the other topological spaces are studied theoretically. Many examples are given to explain the concepts lucidly. The results established in this research paper are new in the field of topology. Full article
(This article belongs to the Special Issue Topological Space and Its Applications)
10 pages, 265 KiB  
Article
Spectrum of Zariski Topology in Multiplication Krasner Hypermodules
by Ergül Türkmen, Burcu Nişancı Türkmen and Öznur Kulak
Mathematics 2023, 11(7), 1754; https://doi.org/10.3390/math11071754 - 6 Apr 2023
Viewed by 1056
Abstract
In this paper, we define the concept of pseudo-prime subhypermodules of hypermodules as a generalization of the prime hyperideal of commutative hyperrings. In particular, we examine the spectrum of the Zariski topology, which we built on the element of the pseudo-prime subhypermodules of [...] Read more.
In this paper, we define the concept of pseudo-prime subhypermodules of hypermodules as a generalization of the prime hyperideal of commutative hyperrings. In particular, we examine the spectrum of the Zariski topology, which we built on the element of the pseudo-prime subhypermodules of a class of hypermodules. Moreover, we provide some relevant properties of the hypermodule in this topological hyperspace. Full article
(This article belongs to the Special Issue Topological Space and Its Applications)
9 pages, 278 KiB  
Article
Fixed Point Results in C🟉-Algebra-Valued Partial b-Metric Spaces with Related Application
by Gunaseelan Mani, Arul Joseph Gnanaprakasam, Ozgur Ege, Ahmad Aloqaily and Nabil Mlaiki
Mathematics 2023, 11(5), 1158; https://doi.org/10.3390/math11051158 - 26 Feb 2023
Cited by 7 | Viewed by 1343
Abstract
In this manuscript, we prove some fixed point theorems on C🟉-algebra-valued partial b-metric spaces by using generalized contraction. We give support and suitable examples of our main results. Moreover, we present a generative application of the main results. Full article
(This article belongs to the Special Issue Topological Space and Its Applications)
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