Paper Title
The Study of Metric Geometry & Metric Space Theory and Its Applications: A Comprehensive Review
Article Identifiers
Registration ID: IJNRD_198797
Published ID: IJNRD2306138
: Click Here to Get
About Hard Copy and Transparent Peer Review Report
Keywords
Distance Function, Euclidean Metric, Metric Geometry, Metric Space Theory, Open and Closed Sets
Abstract
Metric geometry and metric space theory form the backbone of mathematical analysis in the fields of geometry and topology. This research paper presents a comprehensive review of the study of metric geometry and metric space theory, delving into their fundamental concepts, properties, and wide-ranging applications. The paper begins by providing an overview of metric spaces, distance functions, and metrics, establishing the foundational elements necessary for understanding the subsequent discussions. It explores the properties of metric spaces in detail, including completeness, compactness, and connectedness, revealing the rich structural characteristics of these spaces. In-depth exploration is conducted into different types of metrics, such as the Euclidean metric, geodesic metric, and specialized metrics, along with their respective properties and applications. The paper investigates key concepts like isometries, convexity, and curvature, which play pivotal roles in discerning the intrinsic geometry of metric spaces. Furthermore, the research paper delves into metric space theory, covering topics such as open and closed sets, convergence, and continuity. These concepts provide essential tools for analyzing and characterizing metric spaces, enabling researchers to comprehend their intricate properties and behaviors. Importantly, the paper highlights the diverse applications of metric geometry and metric space theory across various fields. It examines their relevance in computer science, data analysis, optimization, machine learning, and network analysis. Concrete examples of applications are discussed, including their utilization in clustering algorithms, nearest neighbor search, graph theory, and shape analysis. These applications demonstrate the practical implications and significant contributions of metric geometry and metric space theory to solving real-world problems and advancing scientific research in numerous domains. In conclusion, this research paper presents a comprehensive review of the study of metric geometry and metric space theory. By elucidating their fundamental concepts, properties, and applications, the paper contributes to the existing body of knowledge in mathematics. It offers valuable insights and serves as a resource for researchers, academics, and practitioners seeking to understand and apply the principles of metric geometry and metric space theory in their respective fields.
Downloads
How To Cite (APA)
Avinash, Dr. G. V. V. Jagannadha Rao, & Omprakash Dewangan (June-2023). The Study of Metric Geometry & Metric Space Theory and Its Applications: A Comprehensive Review. INTERNATIONAL JOURNAL OF NOVEL RESEARCH AND DEVELOPMENT, 8(6), b342-b347. https://ijnrd.org/papers/IJNRD2306138.pdf
Issue
Volume 8 Issue 6, June-2023
Pages : b342-b347
Other Publication Details
Paper Reg. ID: IJNRD_198797
Published Paper Id: IJNRD2306138
Research Area: Engineering
Author Type: Foreign Author
Country: -, -, -
Published Paper PDF: https://ijnrd.org/papers/IJNRD2306138.pdf
Published Paper URL: https://ijnrd.org/viewpaperforall?paper=IJNRD2306138
About Publisher
Journal Name: INTERNATIONAL JOURNAL OF NOVEL RESEARCH AND DEVELOPMENT(IJNRD)
UGC CARE JOURNAL PUBLICATION | ISSN: 2456-4184 | IMPACT FACTOR: 8.76 Calculated By Google Scholar | ESTD YEAR: 2016
An International UGC CARE JOURNAL PUBLICATION, Low Cost, Scholarly Open Access, Peer-Reviewed, Refereed Journal Impact Factor 8.76 Calculate by Google Scholar and Semantic Scholar | AI-Powered Research Tool, Multidisciplinary, Monthly, Multilanguage Journal Indexing in All Major Database & Metadata, Citation Generator
Publisher: IJNRD (IJ Publication) Janvi Wave | IJNRD.ORG | IJNRD.COM | IJPUB.ORG
Copyright & License
© 2026 - Authors hold the copyright of this article. This work is licensed under a Creative Commons Attribution 4.0 International License. and The Open Definition.
This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (CC BY 4.0).
🛡️ Disclaimer: The content, data, and findings in this article are based on the authors’ research and have been peer-reviewed for academic purposes only. Readers are advised to verify all information before practical or commercial use.
The journal and its editorial board are not liable for any errors, losses, or consequences arising from its use.
Publication Timeline
Article Preview: View Full Paper
Call For Paper
IJNRD is a Scholarly Open Access, Peer-Reviewed, Refereed, and UGC CARE Journal Publication with a High Impact Factor of 8.76 (calculated by Google Scholar & Semantic Scholar | AI-Powered Research Tool). It is a Multidisciplinary, Monthly, Low-Cost, and Transparent Peer Review Journal Publication that adheres to the New UGC CARE Transparent Peer-Reviewed Journal Policy and aligns with Scopus Journal Publication standards to ensure the highest level of research quality and credibility.
IJNRD offers comprehensive Journal Publication Services including indexing in all major databases and metadata repositories, Digital Object Identifier (Crossref DOI) assignment for each published article with additional fees, citation generation tools, and full Open Access visibility to enhance global research reach and citation impact.
The INTERNATIONAL JOURNAL OF NOVEL RESEARCH AND DEVELOPMENT (IJNRD) aims to advance applied, theoretical, and experimental research across diverse academic and professional fields. The journal promotes global knowledge exchange among researchers, developers, academicians, engineers, and practitioners, serving as a trusted platform for innovative, peer-reviewed journal publication and scientific collaboration.
Indexing Coverage: Google Scholar, SSRN, ResearcherID-Publons, Semantic Scholar (AI-Powered Research Tool), Microsoft Academic, Academia.edu, arXiv.org, ResearchGate, CiteSeerX, ResearcherID (Thomson Reuters), Mendeley, DocStoc, ISSUU, Scribd, and many other recognized academic repositories.
Transparent Peer Review Journal Publication: IJNRD operates a strict double-blind peer review system managed by 3000+ expert reviewers, ensuring ethical, unbiased, and high-quality review for every research paper.
For Indian Authors : Get a transparent peer review report from Scholar9.com for just ₹1000. View Sample Report
For Foreign Authors : A detailed peer review report is available through Scholar9.com for $20 USD. View Sample Report
Transparent Peer Review Journal Publication
⭐ Transparent Peer Review | 🕵️♂️ Double-Blind | 👨🏫 3000+ Expert Reviewers | 🇮🇳 Report for India Author ₹1000 | 🌐 Report for Foreign Author $20 | 📄 Sample Reports on Scholar9.com | 🌍 High Credibility | ⚖️ Ethical & Unbiased Evaluation
How to submit the paper?
By Our website
Click Here to Submit Paper Online
Recently, the UGC discontinued the UGC-CARE Journal List and introduced new parameters that allow publication in Transparent Peer-Reviewed (Refereed) Journals. IJNRD is Transparent Peer Review Journal Valid As per New UGC Notification.
You can now publish your research paper in IJNRD.ORG. IJNRD is a Transparent Peer-Reviewed Open Access (Refereed Journal), UGC and UGC CARE Approved, Crossref DOI, Multidisciplinary, Impact Factor calculate by Google Scholar. As an International, open-access, and online journal, Publishing with us ensures wider reach, academic credibility, and enhanced recognition for your work.
For more details, refer to the official notice: UGC Public Notice
⭐ Low Cost ₹1570 | 📚 UGC CARE Approved | 🔍 Peer-Reviewed | 🌐 Open Access | 🔗 Crossref DOI & Global Indexing | 📊 Google Scholar Impact Factor | 🧪 Multidisciplinary
Submit Paper Online Call for Paper About IJNRD UGC CARE Approval
Important Dates for Current issue
Paper Submission Open For: February 2026
Current Issue: Volume 11 | Issue 2 | February 2026
Impact Factor: 8.76
Last Date for Paper Submission: Till 28-Feb-2026
Notification of Review Result: Transparent peer review process - your paper is evaluated by experts, and you receive acceptance or rejection updates via email and SMS.
Publication of Paper: Once all documents are submitted, your paper is published without delay, and you can instantly download your certificate and confirmation letter online.
Frequency: Monthly (12 issue Annually).
Journal Type: IJNRD is an international open-access journal offering Low Cost Journal Publication, transparent Peer Review Journal Publication, Crossref DOI, and multidisciplinary research visibility under UGC CARE Approved Journal Publication.
Subject Category: Research Area
Approval, Licenses and Indexing: More Details
Call For Paper - Volume 11 | Issue 2 | February 2026
IJNRD.org offers low-cost journal publication starting at ₹1570 with UGC CARE Approved, refereed, peer-reviewed, open-access publishing. This multidisciplinary monthly journal, available in both online and print formats, features a strong Google Scholar-based impact factor of 8.76, Transparent Peer Review, CrossRef DOI, global indexing, fast publication, and complete metadata for maximum research visibility and citation impact across multidisciplinary domains.
Volume 11 | Issue 2 | February 2026 | IJNRD Transparent Peer Review Certificate | Submit Paper Online
⭐ UGC CARE Approved Refereed Journal | 🔍 Transparent Peer Review | 🌐 Open Access Publishing | 💰 Low-Cost ₹1570 | 🔗 CrossRef DOI & Global Indexing | 📊 Google Scholar Impact Factor 8.76 | 🧪 Multidisciplinary | Online & Print
Submit Paper Online
