Intereting Posts

Binomial Congruence
For a Planar Graph, is it always possible to construct a set of cycle basis, with each and every edge Is shared by at most 2 cycle bases?
How to convert to conjunctive normal form?
Using GAP to compute the abelianization of a subgroup
Involute of a circle – what is the separation distance?
Show that symmetric difference is $A \Delta B = (A \cup B)$ \ $(A\cap B)$
Cyclic Hexagon Circumradius
If $ 3x^2 + 2\alpha xy + 2y^2 + 2ax – 4y + 1 $ can be resolved into two linear factors, then prove the following.
$k$-th moment of product of gaussian and sinc
Tychonov's theorem in countable spaces!?
How do you rebuild your Math skills after college?
How does (21) factor into prime ideals in the ring $\mathbb{Z}$?
What is the standard interpretation of order of operations for the basic arithmetic operations?
Largest idempotent
Liapunov's Inequality for $L_p$ spaces

I need an example for a compact, Hausdorff, separable space which is not first-countable.

I tried to look for it for some time without success…

- nonstandard example of smooth function which fails to be analytic on $\mathbb{R}$
- How many points does Stone-Čech compactification add?
- $^{\mathbb{N}}$ with respect to the box topology is not compact
- Example of different topologies with same convergent sequences
- give a counterexample of monoid
- Prove that a compact metric space is complete.
- Proving that the Union of Two Compact Sets is Compact
- Is a semigroup $G$ with left identity and right inverses a group?
- Examples of non-measurable sets in $\mathbb{R}$
- Accidents of small $n$

The space $I^I$ (i.e., product of $\mathfrak c$-many copies of the unit interval $I=[0,1]$ is a compact Hausdorff space.

It is not first-countable, see here: Uncountable Cartesian product of closed interval

It is separable by Hewitt-Marczewski-Pondiczery theorem,

see here: On the product of $\mathfrak c$-many separable spaces

- differential system on the torus
- Expected number of times Random Walk crosses 0 line.
- Archimedean Property and Real Numbers
- What tools are used to show a type of convergence is or is not topologizable?
- maximum estimator method more known as MLE of a uniform distribution
- Prove that $\sin(\sqrt{x})$ is not periodic, without using derivation
- Counting integer partitions of n into exactly k distinct parts size at most M
- Domain is Hausdorff if image of covering map is Hausdorff
- $C^1$ is closed in $C$
- Find integer in the form: $\frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b}$
- Can $\ln(x)=\lim_{n\to\infty} n\left(x^{\frac1{n}}-1 \right)$ be expressed as an infinite telescoping product?
- Sequence Of Primes
- Approximation to $ \sqrt{2}$
- Convergence rate of Newton's method
- A function that is neither O(n) nor Ω(n).