Topological Algebras and Related Topics

Dear Colleagues,

Topological algebras arise naturally when algebraic structures are equipped with compatible topological, uniform, or metric structures, leading to deep interactions between algebra, topology, analysis, and logic. Classical examples include topological groups and Lie groups, topological vector spaces, and algebras studied in functional analysis. In recent years, methods from mathematical logic, particularly descriptive set theory, have played an increasingly important role in the study of topological and algebraic structures, offering refined tools to investigate definability, complexity and regularity properties of sets, functions, and algebraic operations.

Recent advances in set-theoretic topology, generalized metric spaces, and descriptive set-theoretic techniques have further clarified the impact of axioms, cardinal invariants, and definability constraints on problems involving continuity, compactness, completeness, and duality. These developments highlight the foundational character of the area and its strong connection with the aims and scope of Axioms.

We are pleased to invite you to contribute to this Special Issue devoted to topological algebras and related topics.

This Special Issue aims to provide a focused yet comprehensive platform for original research articles and high-quality surveys on algebraic structures equipped with topological or uniform frameworks. Particular emphasis is placed on axiomatic approaches, structural properties, and the interaction between algebraic operations and topological or logical constraints. Contributions employing tools from mathematical logic, including descriptive set theory and related areas, are especially welcome.

The topic fits naturally within the scope of Axioms, as it promotes foundational viewpoints, abstract frameworks, and unifying principles across topology, algebra, analysis, and logic. The scope is designed to be sufficiently broad to attract diverse contributions while remaining coherent around the central theme of topological–algebraic interaction.

In this Special Issue, original research articles and review papers are welcome. Research areas may include (but are not limited to) the following:

• Topological groups and Lie groups;
• Topological and locally convex vector spaces;
• Topological and locally compact algebras;
• Set-theoretic topology and cardinal invariants;
• Descriptive set theory in topological and algebraic contexts;
• Logical and definability aspects of topological structures;
• Generalized metric and uniform spaces related to algebraic structures;
• Duality, compactness, and completeness phenomena;
• Applications to functional analysis and harmonic analysis.

We look forward to receiving your contributions.

Prof. Dr. Wei He
Dr. Dekui Peng
Dr. Víctor Hugo Yañez
Dr. Ziqin Feng
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 250 words) can be sent to the Editorial Office for assessment.

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.

• topological algebras
• topological groups
• lie groups
• set-theoretic topology
• descriptive set theory
• mathematical logic
• generalized metric spaces
• topological vector spaces
• functional analysis