Solutions to Selected Exercises
On this page, I have kept some of the solutions to some problems from various books and problems that I encountered from various sources for reference. Kindly let me know if there is an error at any place. I will try to fix that.
Solutions to Real Analysis, Fourth Edition, by H. Royden and P. Fitzpatrick
These notes contain hints and (sometimes) solutions to the exercises in the book Real Analysis by H. Royden and P. Fitzpatrick. Some portions of the notes may contain some details added to the theory part of the book. I will keep updating the notes attached here. For some of the answers, I had to look at different web-based discussions and resources. Please write me an email if you find errors in the solutions or any typographical mistakes.
In Section 2.7, I have given a detailed and rigorous account of the Cantor set and the Cantor function. This could be pretty useful to beginners. Also, in the exercises of Section 3.1, I have discussed the properties of the Borel measurable functions in detail, which is another theoretical highlight of the material.
Solutions to Selected Exercises in Algebraic Topology
These notes contain hints and (sometimes) solutions to the exercises from Sections 51-82 in the book Topology by J. Munkres and exercises from the book Algebraic Topology by A. Hatcher. Some portions of the notes may contain some details added to the theory part of the book. I also plan to add any relevant exercises from the previous section at some later point of time. I will keep updating the notes attached here. For some of the answers, I had to look at different web-based discussions and resources. Please write me an email if you find errors in the solutions or any typographical mistakes. Later I plan to add solutions to exercises from the book Elements of Algebraic Topology by J. Munkres in the third part of this note.
Problems from "An Introduction to Algebraic Topology" by Joseph J. Rotman
These notes contain hints and (sometimes) solutions to the exercises in the book An Introduction to Algebraic Topology by Joseph J. Rotman. Some of the notes may contain some details added to the theory part of the book. For some of the answers, I had to look at different web-based discussions and resources.
Chapter 1: Some Basic Topological Notions
Chapter 3: The Fundamental Group
Chapter 5: Long Exact Sequences
Chapter 6: Excision and Applications