Intereting Posts

Proof of a Ramanujan Integral
Show that $\sum\limits_{i=0}^{n/2} {n-i\choose i}2^i = \frac13(2^{n+1}+(-1)^n)$
Derivative of the nuclear norm with respect to its argument
$\lim_{x \to 2} \frac{x^{2n}-4^n}{x^2-3x+2}$
The Greatest Common Divisor of All Numbers of the Form $n^a-n^b$
Counterexamples in $R$-modules products and $R$-modules direct sums and $R$-homomorphisms (Exemplification)
($n$-dimensional) Inverse Fourier transform of $\frac{1}{\| \mathbf{\omega} \|^{2\alpha}}$
Path components or connected components?
Prove that Gauss map on M is surjective
The interval $$ is not the disjoint countable union of closed intervals.
General Isomorphism, for all algebraic structures
$M$ is a simple module if and only if $M \cong R/I$ for some $I$ maximal ideal in $R$.
Present a function with specific feature
If $a\in R$ and the equation $-3(x-\lfloor x \rfloor)^2+2(x-\lfloor x \rfloor)+a^2=0$ has no integral solution,then all possible values of $a$
How to show that $\sin(n)$ does not converge?

I have started reading the book *Topology Without Tears* by Sidney A. Morris. I have read the first chapter and so far it reads well. However, the name of the book is a bit deceiving and makes me think it is not a book to rigorously learn topology. Has anyone read (or) used the book? If so, could you let me know if it is a nice book to start with? If not, could you let me know what book I should use to learn topology? (I would prefer a free book available online. It is quite expensive to buy a good book in India. However, if it is “the” book and I must have if I want to learn topology then I shall consider buying it.)

Thanks,

Adhvaitha

- Error in book's definition of open sets in terms of neighborhoods?
- Relationships between AC, Ultrafilter Lemma/BPIT, Non-measurable sets
- Graph of a function homeomorphic to a space implies continuity of the map?
- variant on Sierpinski carpet: rescue the tablecloth!
- Why is one “$\infty$” number enough for complex numbers?
- Representation of $S^{3}$ as the union of two solid tori

- Continuous mapping on a compact metric space is uniformly continuous
- Every subnet of $(x_d)_{d\in D}$ has a subnet which converges to $a$. Does $(x_d)_{d\in D}$ converge to $a$?
- Uniform convergence of functions, Spring 2002
- Why is $^\mathbb{N}$ not countably compact with the uniform topology?
- How to prove that given set is a connected subset of the space of matrices?
- example of a continuous function that is closed but not open
- sequential convergence and continuity
- Tietze extension theorem for complex valued functions
- Path-connected and locally connected space that is not locally path-connected
- An introduction to Khovanov homology, Heegaard-Floer homology

Yes, it’s a good book to learn topology. The author takes some space to talk about intuition, but all definitions, theorems, proofs are rigorous.

(Side note: Looking at your user profile, you might be falling in the calculus trap. Please read this article.)

- In Fitch, is a symbol not in a specified language automatically free?
- Given two subspaces $U,W$ of vector space $V$, how to show that $\dim(U)+\dim(W)=\dim(U+W)+\dim(U\cap W)$
- Examine if function $f:\mathbb{R^2}\rightarrow \mathbb{R^2}$ which is defined as $f(x,y)=(2x-y,x-4y)$ is bijective. If bijective, find $f^{-1}$.
- Help with proof using induction: $1 + \frac{1}{4} + \frac{1}{9}+\cdots+\frac{1}{n^2}\leq 2-\frac{1}{n}$
- Let $E$ be a Banach space, prove that the sum of two closed subspaces is closed if one is finite dimensional
- Factoring with fractional exponents
- If$(ab)^n=a^nb^n$ & $(|G|, n(n-1))=1$ then $G$ is abelian
- Finding all solutions of the Pell-type equation $x^2-5y^2 = -4$
- How to compute the sum $ 1+a(1+b)+a^2(1+b+b^2)+a^3(1+b+b^2+b^3)+\cdots$
- Proving that infinite union of simple groups is also simple group
- Product rule for scalar-vector product
- Homotopy invariance of the Picard group
- What does “homomorphism” require that “morphism” doesn't?
- Importance of Constructible functions
- Can we extend the definition of a homomorphism to binary relations?