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Axioms
Special Issues
Topics in General Topology and Applications
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Topics in General Topology and Applications

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Geometry and Topology".

Deadline for manuscript submissions: 31 May 2025 | Viewed by 4324

Special Issue Editor

Prof. Dr. Ljubiša D. R. Kočinac

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Guest Editor
Faculty of Sciences and Mathematics, University of Niš, 18000 Niš, Serbia
Interests: general topology; mathematical analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The goal of this Special Issue is to collect articles reflecting new trends and lines of theoretical investigation in all branches of general topology and progress in applications of topological methods and techniques in various mathematical disciplines and other sciences.

Although all topics in general topology are welcome, we can specify a few selected themes of interest: cardinal invariants, function spaces, hyperspaces, topological algebras, functors in general topology, dimension theory, convergence, selection principles, game theory in topology, fuzzy topology, soft topology and its applications, digital topology, combinatorial topology, categorical methods in topology, uniform spaces, fixed point theory, and topological methods in analysis.

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

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. Axioms is an international peer-reviewed open access monthly 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 2400 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

  • cardinal invariants
  • function spaces
  • hyperspaces
  • topological algebras
  • functors in general topology
  • dimension theory
  • selection principles
  • game theory in topology
  • fuzzy topology
  • soft topology and its applications
  • digital topology
  • combinatorial topology
  • categorical methods in topology
  • uniform spaces
  • fixed point theory
  • topological methods in analysis

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

Published Papers (5 papers)

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Research

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21 pages, 382 KiB  
Article
Idealizing Rough Topological Structures Generated by Several Types of Maximal Neighborhoods and Exploring Their Applications
by Mona Hosny
Axioms 2025, 14(5), 333; https://doi.org/10.3390/axioms14050333 - 27 Apr 2025
Viewed by 96
Abstract
Several different topologies utilizing ideals are created and compared with previous topologies. The results show that the previous ones are weaker than the current ones and that the current ones are stronger. The merits of these topologies are proposed, and the smallest and [...] Read more.
Several different topologies utilizing ideals are created and compared with previous topologies. The results show that the previous ones are weaker than the current ones and that the current ones are stronger. The merits of these topologies are proposed, and the smallest and largest among them are identified; this merit distinguishes the present study from previous ones. Afterwards, these topologies are employed to conduct more in-depth investigations on broadened rough sets. The proposed approximate models are particularly significant as applied to rough sets because they diminish vagueness and uncertainty compared to prior models. Moreover, the proposed models stand out from their predecessors because they can compare all types of approximations, display all the features described by Pawlak, and possess the property of monotonicity across any relations. Furthermore, a medical application is showcased to emphasize the significance of the current findings. Additionally, the advantages of the adopted approach are examined, alongside an evaluation of its limitations. The paper wraps up with the essential features of the proposed manner and recommend avenues for future research. Full article
(This article belongs to the Special Issue Topics in General Topology and Applications)
16 pages, 306 KiB  
Article
On Topologies Induced by Ideals, Primals, Filters and Grills
by Milan Matejdes
Axioms 2024, 13(10), 698; https://doi.org/10.3390/axioms13100698 - 8 Oct 2024
Viewed by 871
Abstract
In this paper, one-to-one correspondences and equivalences between ideals, primals, filters and grills are introduced. It is shown that the local functions and the topological spaces induced by them are the same. From this point of view, the topological properties of one topology [...] Read more.
In this paper, one-to-one correspondences and equivalences between ideals, primals, filters and grills are introduced. It is shown that the local functions and the topological spaces induced by them are the same. From this point of view, the topological properties of one topology can be derived from the topological properties that are valid in the corresponding topology. Full article
(This article belongs to the Special Issue Topics in General Topology and Applications)
23 pages, 487 KiB  
Article
The Kauffman Bracket Skein Module of S1 × S2 via Braids
by Ioannis Diamantis
Axioms 2024, 13(9), 617; https://doi.org/10.3390/axioms13090617 - 11 Sep 2024
Viewed by 933
Abstract
In this paper, we present two different ways for computing the Kauffman bracket skein module of S1×S2, KBSMS1×S2, via braids. We first extend the universal Kauffman bracket type invariant V for knots [...] Read more.
In this paper, we present two different ways for computing the Kauffman bracket skein module of S1×S2, KBSMS1×S2, via braids. We first extend the universal Kauffman bracket type invariant V for knots and links in the Solid Torus ST, which is obtained via a unique Markov trace constructed on the generalized Temperley–Lieb algebra of type B, to an invariant for knots and links in S1×S2. We do that by imposing on V relations coming from the braid band moves. These moves reflect isotopy in S1×S2 and they are similar to the second Kirby move. We obtain an infinite system of equations, a solution of which is equivalent to computing KBSMS1×S2. We show that KBSMS1×S2 is not torsion free and that its free part is generated by the unknot (or the empty knot). We then present a diagrammatic method for computing KBSMS1×S2 via braids. Using this diagrammatic method, we also obtain a closed formula for the torsion part of KBSMS1×S2. Full article
(This article belongs to the Special Issue Topics in General Topology and Applications)
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13 pages, 316 KiB  
Article
On the Čech-Completeness of the Space of τ-Smooth Idempotent Probability Measures
by Ljubiša D. R. Kočinac, Adilbek A. Zaitov and Muzaffar R. Eshimbetov
Axioms 2024, 13(8), 569; https://doi.org/10.3390/axioms13080569 - 21 Aug 2024
Viewed by 785
Abstract
For the set I(X) of probability measures on a compact Hausdorff space X, we propose a new way to introduce the topology by using the open subsets of the space X. Then, among other things, we give a [...] Read more.
For the set I(X) of probability measures on a compact Hausdorff space X, we propose a new way to introduce the topology by using the open subsets of the space X. Then, among other things, we give a new proof that for a compact Hausdorff space X, the space I(X) is also a compact Hausdorff space. For a Tychonoff space X, we consider the topological space Iτ(X) of τ-smooth idempotent probability measures on X and show that the space Iτ(X) is Čech-complete if and only if the given space X is Čech-complete. Full article
(This article belongs to the Special Issue Topics in General Topology and Applications)

Review

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17 pages, 323 KiB  
Review
Recent Progress on Point-Countable Covers and Sequence-Covering Mappings
by Shou Lin and Jing Zhang
Axioms 2024, 13(10), 728; https://doi.org/10.3390/axioms13100728 - 21 Oct 2024
Viewed by 836
Abstract
This paper is dedicated to the memory of Professor Gary Gruenhage (1947–2023). This survey introduces the formation and early development of the topic of point-countable covers and sequence-covering mappings, and lists the recent progress of 38 questions on this topic proposed before 2015, [...] Read more.
This paper is dedicated to the memory of Professor Gary Gruenhage (1947–2023). This survey introduces the formation and early development of the topic of point-countable covers and sequence-covering mappings, and lists the recent progress of 38 questions on this topic proposed before 2015, which involve the theory of generalized metric spaces. These questions are related to point-countable covers and sequence-covering mappings, including point-countable covers with certain networks, sequence-covering mappings, images of metric spaces, and hereditarily closure-preserving families. Full article
(This article belongs to the Special Issue Topics in General Topology and Applications)
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