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Axioms
Special Issues
General Topology and Fuzzy Topology
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General Topology and Fuzzy Topology

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

Deadline for manuscript submissions: closed (31 December 2024) | Viewed by 3732

Special Issue Editor

Dr. Francisco Gallego Lupianez

E-Mail Website
Guest Editor
Department of Mathematics, Universidad Complutense, Madrid, Spain
Interests: general topology; fuzzy topology
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Paracompactness is a concept introduced by J. Dieudonné in 1944. It includes compact and metrizable spaces, and has important applications in differential topology, differential geometry and functional analysis.

In addition to paracompactness in the strict sense, other variants of this concept have emerged. It is a very fruitful field of research and there are very recent publications on paracompactness-type properties. We invite authors to submit papers about this topic.

On the other hand, Zadeh's fuzzy sets provide a more accurate representation of reality than the classical mathematical representation based on two-valued logic. Fuzzy sets have been applied in various branches of mathematics, including topology.

This Special Issue will publish original research papers (and well-written reviews) in the field of fuzzy topology. We hope that this Special Issue will be valuable to specialists in this topic.

We invite authors to submit papers that will stimulate the continuing efforts to provide new results on fuzzy topological spaces in the sense of Chang, Lowen, and Michalek. We also welcome papers on intuitionistic fuzzy topological spaces and neutrosophic topological spaces.

Dr. Francisco Gallego Lupianez
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

  • general topology
  • covering properties
  • paracompactness
  • fuzzy topology
  • intuitionistic fuzzy topological spaces
  • neutrosophic topology

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Published Papers (3 papers)

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Research

13 pages, 288 KiB  
Article
On the Axiomatic of GV-Fuzzy Metric Spaces and Its Completion
by Valentín Gregori, Juan-José Miñana, Bernardino Roig and Almanzor Sapena
Axioms 2025, 14(2), 89; https://doi.org/10.3390/axioms14020089 - 25 Jan 2025
Viewed by 614
Abstract
The concept of fuzzy metric space introduced by Kramosil and Michalek was later slightly modified by George and Veeramani who imposed three additional restrictions on it. A significant difference between these two concepts of fuzzy metrics is that fuzzy metric spaces in the [...] Read more.
The concept of fuzzy metric space introduced by Kramosil and Michalek was later slightly modified by George and Veeramani who imposed three additional restrictions on it. A significant difference between these two concepts of fuzzy metrics is that fuzzy metric spaces in the sense of George and Veeramani do not admit completion, in general. This paper is devoted to go into detail on completable fuzzy metric spaces by means of the study of the impact on the completion of each one of the restrictions imposed by George and Veeramani in their definition of fuzzy metric. In this direction, we characterize those completable fuzzy metric spaces, in which just one of the three restrictions imposed by George and Veeramani is required. Various examples illustrate and justify the main results. Full article
(This article belongs to the Special Issue General Topology and Fuzzy Topology)
21 pages, 373 KiB  
Article
Extending L-Topologies to Bipolar L-Fuzzy Topologies
by Alexander Šostak and Ingrīda Uļjane
Axioms 2024, 13(9), 582; https://doi.org/10.3390/axioms13090582 - 27 Aug 2024
Viewed by 604
Abstract
We develop a model that allows for the extension of an L-topology τ on a set X (i.e., τ⊆LX) to a bipolar L-fuzzy topology T on this set (i.e., T:LX→L). This [...] Read more.
We develop a model that allows for the extension of an L-topology τ on a set X (i.e., τ⊆LX) to a bipolar L-fuzzy topology T on this set (i.e., T:LX→L). This model is based on the use of an additional algebraic structure on a complete infinitely distributive lattice L, and the derived lattice L obtained by “bipolarizing” the original lattice L. The properties of the obtained bipolar L-fuzzy topology are studied. A number of examples show how the choice of algebraic structure on L affects the resulting bipolar L-fuzzy topology. In particular, we consider the case when the original lattice L is enriched with a structure of a Girard monoid. In this case our construction becomes most transparent. In addition, the relationship between the extended bipolar L-fuzzy topology and the corresponding extended bipolar L-fuzzy co-topology in this case becomes dual. In the last section we examine the proposed model from the categorical point of view. Full article
(This article belongs to the Special Issue General Topology and Fuzzy Topology)
22 pages, 352 KiB  
Article
Vector-Valued Fuzzy Metric Spaces and Fixed Point Theorems
by Satish Shukla, Nikita Dubey and Juan-José Miñana
Axioms 2024, 13(4), 252; https://doi.org/10.3390/axioms13040252 - 10 Apr 2024
Viewed by 1750
Abstract
The purpose of this paper is to generalize the concept of classical fuzzy set to vector-valued fuzzy set which can attend values not only in the real interval [0, 1], but in an ordered interval of a Banach [...] Read more.
The purpose of this paper is to generalize the concept of classical fuzzy set to vector-valued fuzzy set which can attend values not only in the real interval [0, 1], but in an ordered interval of a Banach algebra as well. This notion allows us to introduce the concept of vector-valued fuzzy metric space which generalizes, extends and unifies the notion of classical fuzzy metric space and complex-valued fuzzy metric space and permits us to consider the fuzzy sets and metrics in a larger domain. Some topological properties of such spaces are discussed and some fixed point results in this new setting are proved. Multifarious examples are presented which clarify and justify our claims and results. Full article
(This article belongs to the Special Issue General Topology and Fuzzy Topology)
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