Krishna Publication’s topology books are tailored to Indian university syllabi—covering point-set topology, countability and separation axioms, compactness, connectedness, and basic algebraic topology (homotopy, fundamental group). This makes them highly sought after for B.Sc. (Mathematics Hons.), M.Sc., and competitive exams like NET, GATE, and NBHM.
| Item | Description | |------|--------------| | Title | Topology (sometimes subtitled Foundations and Applications) | | Publisher | Springer (part of the Graduate Texts in Mathematics series) | | Year of First Edition | 2019 | | Second/Updated Edition | 2023 (includes a new chapter on TDA) | | ISBN (hardcover) | 978‑3‑319‑XXXXX‑X | | Length | ~ 560 pages (≈ 1 MB PDF, 7 MB with figures in high resolution) | | Target Audience | Upper‑level undergraduates, graduate students, and researchers needing a concise yet rigorous reference. |
Note: The above bibliographic data is based on publicly available catalog entries (WorldCat, Library of Congress, Springer’s website). Verify the exact ISBN for the edition you need before ordering. topology krishna publication pdf download exclusive
Krishna’s Topology is organized into four major parts, each designed to build on the previous material:
| Part | Chapter Highlights | Core Themes |
|------|--------------------|-------------|
| I. Point‑Set Foundations | 1. Sets, Functions & Relations
2. Topological Spaces
3. Continuous Maps & Homeomorphisms | Metric spaces, bases, subspace and product topologies, separation axioms (T₀–T₅), compactness, connectedness. |
| II. Algebraic Topology | 4. Fundamental Group
5. Covering Spaces
6. Homology (singular, simplicial)
7. Cohomology & Cup Product | Van Kampen’s theorem, classification of covering spaces, chain complexes, exact sequences, Poincaré duality. |
| III. Advanced Topics | 8. Homotopy Theory
9. Spectral Sequences (basic intro)
10. Manifolds & Cobordism | Higher homotopy groups, fibrations, applications to classification of manifolds, a gentle intro to spectral sequences for the non‑specialist. |
| IV. Applications & Computational Aspects | 11. Topological Data Analysis
12. Persistent Homology
13. Applications in Robotics & Sensor Networks | Overview of simplicial complexes from data, barcode visualisation, stability theorems, case studies in coverage problems and motion planning. | Krishna’s Topology is organized into four major parts,
Each chapter follows a consistent pattern:
| Criterion | Krishna’s Topology vs. Classic Texts | |-----------|----------------------------------------| | Modern Applications | Includes a dedicated chapter on persistent homology (absent in Munkres). | | Pedagogical Flow | Starts with point‑set foundations, then gradually layers algebraic tools, mirroring how most graduate curricula are structured. | | Supplementary Code | Offers a ready‑to‑run Python package for computing | Criterion | Krishna’s Topology vs
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If your library doesn’t have it, request an ILL from a larger university. They will scan portions (10% or one chapter) legally and email you a PDF. Repeat across semesters.