Intereting Posts

Find all reals $a, b$ for which $a^b$ is also real
Does the inverse of a polynomial matrix have polynomial growth?
In how many ways can n couples (husband and wife) be arranged on a bench so no wife would sit next to her husband?
Proving the Existence of Triangle by Induction
Finding a point on Archimedean Spiral by its path length
Prove that subsequence converges to limsup
If $f\colon \mathbb{R} \to \mathbb{R}$ is such that $f (x + y) = f (x) f (y)$ and continuous at $0$, then continuous everywhere
On the existence of field morphisms
Is every noninvertible matrix a zero divisor?
Where can I learn about the lattice of partitions?
Factorial of a non-integer number
Prove that equation has exactly 2 solutions
The identity cannot be a commutator in a Banach algebra?
The cartesian product $\mathbb{N} \times \mathbb{N}$ is countable
What is the Arg of $\sqrt{(t-1)(t-2)}$ at the point $t=0$?

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

- Why sequential continuity from $E$ to $E'$ implies continuity?
- Number of path components of a function space
- Does a homeomorphism between two compact metric spaces preserve open balls?
- $S^3$ $\cong$ $D^2\times S^1\bigsqcup_{S^1\times S^1} S^1\times D^2$?
- A valid proof for the invariance of domain theorem?
- Is a covering space of a completely regular space also completely regular

- How do I show that $f: [0,1) \to S^1$, $f(t) = (\cos(2\pi t), \sin(2\pi t))$ is not a homeomorphism?
- If $a\in \mathrm{clo}(S)$, does it follow that there exists a sequence of points in $S$ that converges to $a$?
- Every separable metric space has cardinality less than or equal to the cardinality of the continuum.
- Show that $ \cap \mathbb{Q}$ is not compact in $$
- How to prove that $\mathbb R^\omega$ with the box topology is completely regular
- Countable neighborhood base at zero in a topological vector space
- Metric space and continuous function
- Product of spaces is a manifold with boundary. What can be said about the spaces themselves?
- Stereographic projection is a homeomorphism $S^n \setminus \{p\} \to \mathbb{R}^n$
- How to prove that this set is closed?

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.)

- $\sum \limits_{n=1}^{\infty}{a_n^2}$ converges $\implies \sum \limits_{n=1}^{\infty}{\dfrac{a_n}{n}}$
- The unit square stays path-connected when you delete a cycle-free countable family of open segments?
- Counting Functions or Asymptotic Densities for Subsets of k-almost Primes
- Is there an elementary method for evaluating $\displaystyle \int_0^\infty \frac{dx}{x^s (x+1)}$?
- Find lim:$\lim_{x\to0} \frac{\tan(\tan x) – \sin(\sin x)}{\tan x -\sin x}$
- Do all polynomials of even degree start by decreasing as you plot from $-\infty$ upward?
- Connected-ness of the boundary of convex sets in $\mathbb R^n$ , $n>1$ , under additional assumptions of the convex set being compact or bounded
- Product of all numbers in a given interval $$
- Circles and tangents and circumcircles
- In combinatorics, how can one verify that one has counted correctly?
- How many elements are there in the group of invertible $2\times 2$ matrices over the field of seven elements?
- If $\alpha=\frac{2\pi}{7}$,prove that $\sin\alpha+\sin2\alpha+\sin4\alpha=\frac{\sqrt7}{2}$
- Solving $\cos x=x$
- Existence of a subset $S\subset\mathbb R$ s.t. $\forall a<b$, $S\cap $ has Lebesgue measure $(b-a)/2$?
- Interesting puzzle about a sphere and some circles