Name: Precize Topology MCQs For UGC CSIR NET Included For MSc Mathematics Panjab University Chandigarh
Brand: Amit Book Depot
Price: 295 INR
Availability: InStock

Master Topology with Precision: The Ultimate MCQ Guide for UGC NET, CSIR NET, and MSc Mathematics

Precise Topology MCQs for UGC CSIR NET Included for MSc Mathematics Panjab University Chandigarh is a definitive and specialized academic resource meticulously crafted by Dr. G. S. Sandhu, Vanita, and Parveen Ansari. Published by First World Publications, this book is an indispensable tool for postgraduate students and competitive exam aspirants aiming to achieve mastery in topology. It is specifically designed to align with the syllabi of prominent examinations like the UGC NET for Mathematical Sciences, the CSIR NET for Mathematics, and the compulsory Topology course (MATH-618S) for MSc Mathematics at Panjab University, Chandigarh.

This comprehensive guide serves a dual purpose: it is both a structured book for mastering core topology concepts and an extensive question bank for rigorous self-assessment. The content is systematically organized to build from foundational principles to advanced theorems, ensuring a logical and deep understanding of the subject. The book meticulously covers the entire scope as outlined in the standard reference, Topology by James R. Munkres, making it a perfect companion for university studies and competitive preparation alike.

Comprehensive and Structured Content Coverage

The book begins with preliminaries to solidify your foundational knowledge before progressing through all critical topics in point-set topology. The chapters are carefully sequenced to mirror a standard university curriculum:

1. Core Concepts: Dive deep into Topological Spaces, Bases for a Topology, Continuous Functions, and various fundamental constructs.

2. Advanced Topologies: Gain proficiency in constructing and analyzing different topological spaces, including the product topology, box topology, metric topology, and quotient topology.

3. Key Properties: Master the essential characteristics of topological spaces with detailed chapters on Connectedness and Compactness, including their variants like local connectedness and limit point compactness.

4. Convergence and Countability: Understand advanced concepts like nets for convergence in general topological spaces and the countability axioms.

5. Separation and Metrization: Thoroughly explore the Separation Axioms (T0, T1, T2, T3, T4), Normal Spaces, and profound results such as the Urysohn Lemma, Tietze Extension Theorem, and the Urysohn Metrization Theorem.

Targeted Exam Preparation with Extensive Practice

A significant portion of this book is dedicated to a vast collection of Multiple-Choice Questions (MCQs) specifically curated for the UGC NET and CSIR NET examinations. These MCQs are designed to test conceptual clarity, application skills, and problem-solving speed. Practicing with these questions will help aspirants identify their strengths and weaknesses, manage time effectively during the actual exam, and familiarize themselves with the pattern and difficulty level of questions asked in these highly competitive tests.

Perfectly Aligned with University Syllabus

For students of MSc Mathematics at Panjab University, Chandigarh, this book is an invaluable resource for the compulsory course MATH-618S: Topology. The chapter-wise breakdown directly corresponds to the units prescribed in the syllabus, covering everything from Unit I (Topological Spaces, Continuous Functions, Product and Quotient Topologies, Connectedness) to Unit II (Compactness, Nets, Countability, Separation Axioms, and Major Theorems). The internal structure of the book, with its clear explanations and solved problems, provides the perfect study material for scoring high in both internal assessments and the final theory papers.

Have Doubts Regarding This Product ? Ask Your Question

Q1

Is this book suitable for someone starting to learn Topology from scratch?

A1

Yes, the book begins with a "Preliminaries" chapter to build foundational knowledge and progresses logically from basic to advanced concepts, making it accessible for dedicated beginners.
Q2

How does this book help specifically with the UGC NET/CSIR NET exam?

A2

It contains a dedicated section with numerous MCQs modeled on the pattern and difficulty of these exams, helping you practice and improve your speed and accuracy.
Q3

Is the content of this book aligned with the standard reference book "Topology" by James R. Munkres?

A3

Absolutely. The authors have structured the content to cover the scope of the relevant sections from Munkres' "Topology," as specified in the Panjab University and NET syllabi.
Q4

Does this book cover proofs of major theorems like Urysohn's Lemma and the Tietze Extension Theorem?

A4

Yes, the book provides explanations and insights into major theorems, including the Urysohn Lemma, Tietze Extension Theorem, Urysohn Metrization Theorem, and Tychonoff Theorem, which are crucial for both university exams and NET.
Q5

I am a student of MSc Mathematics at a university other than Panjab University. Is this book still useful for me?

A5

Yes, the core topics in Topology are standardized across most universities. The comprehensive coverage of fundamental and advanced topics makes it a valuable resource for any MSc Mathematics student.
Q6

Does the book include topics like Nets and the Box Topology, which are sometimes omitted in introductory courses?

A6

Yes, it includes dedicated chapters on both Nets and the Box Topology, providing coverage of these important, advanced concepts.
Q7

How is the book structured for the Panjab University MATH-618S syllabus?

A7

The chapter sequence directly maps onto the two units of the Panjab University syllabus, making it easy for students to follow their course structure.
Q8

Can this book be used as the primary textbook for my MSc Topology course?

A8

While it is an excellent companion and problem-solving guide, you should confirm with your course instructor if it can serve as the primary text alongside the standard reference (Munkres).
Q9

Is the Metric Topology covered adequately?

A9

Yes, Chapter 4 is specifically dedicated to The Metric Topology, which is a fundamental concept in the study of topological spaces.
Q10

Does the book cover both "Connectedness" and "Compactness" in detail?

A10

Yes, there are full, dedicated chapters on Connectedness and Compactness, exploring various aspects like local connectedness, components, limit point compactness, and local compactness.

0.00

0 Overall Rating

5

0
4

0
3

0
2

0
1

0

Try this product & share your review & thoughts

0. Preliminaries

1. Topological Spaces

2. Continuous Functions

3. Product and Box Topology

4. The Metric Topology

5. Quotient Topology

6. Connectedness

7. Compactness

8. Nets

9. Countability

10. Separation Axioms

MCQs for UGC NET

Latest Syllabus Of Topology MCQs For UGC CSIR NET Included For MSc Mathematics Panjab University (PU) Chandigarh

MATH-618S: TOPOLOGY

(COMPULSORY COURSE)

Total Marks: 100

Theory: 80

Marks for Internal Assessment: 20 Marks

Time: 3 hrs.

Note:

1. The question paper will consist of 9 questions. Candidates will attempt a total of five questions.

2. Question No. 1 is compulsory and will consist of short answer-type questions covering the whole syllabus.

3. There will be four questions from each unit, and the candidates will be required to attempt two questions from each unit.

4. All questions carry equal marks.

UNIT – I

Topological spaces, bases for a topology, the order topology, the product topology on X × Y, the subspace topology, closed sets and limit points, continuous functions, the product topology, the metric topology, and the quotient topology.

[Scope as in the relevant sections in Chapters 2 & 3 of the book ‘Topology,’ second edition, 2002, by James R. Munkres.]

Connected spaces, connected subspaces of the real line, components, and local connectedness.

UNIT-II

Compact spaces, the compact space of the real line, limit point compactness, local compactness, and nets.

[Scope as in the relevant sections in Chapter 3 of the book ‘Topology,’ second edition, 2002, by James R. Munkres.]

The countability axioms, the separation axioms, normal spaces, the Urysohn Lemma, the Urysohn Metrization Theorem, the Tietze Extension Theorem, and the Tychonoff Theorem.

[Scope as in the relevant sections in Chapters 4 and 5 of the book ‘Topology,’ second edition, 2002, by James R. Munkres.]