Intereting Posts

Prove that a group generated by two elements of order $2$, $x$ and $y$, is isomorphic to $D_{2n}$, where $n = |xy|.$
Least number of weights required to weigh integer weights
How can I solve for a single variable which occurs in multiple trigonometric functions in an equation?
Show that $\langle,V\rangle = -\langle U,\rangle$ for bi-invariant metric in Lie group
Two Fredholm operators A and B have the same index iff there is an invertible operator C s.t. A-BC is compact
Prove that two paths on opposing corners of the unit square must cross.
Why is the Taylor expansion of $\cos$ decreasing?
upper bound on partial sums of Dirichlet character
A proof of $\int_{0}^{1}\left( \frac{\ln t}{1-t}\right)^2\,\mathrm{d}t=\frac{\pi^2}{3}$
Why is it linearly dependent when the linear combination is zero only with none zero coefficients in 3D?
Slightly changing the formal definition of continuity of $f: \mathbb{R} \to \mathbb{R}$?
“Random” generation of rotation matrices
All ideals of a subring of $\Bbb Q$
Why Not Define $0/0$ To Be $0$?
Scale invariant definition of the Sobolev norm $\|\|_{m,\Omega}$ for $H^m(\Omega)$

Let X be a compact metrizable space. Would you help me to prove that X has a countable basis. Thanks.

- Natural derivation of the complex exponential function?
- Homeomorphism theorem
- Is the Baire space $\sigma$-compact?
- Proving that the set of limit points of a set is closed
- Confusion Regarding Munkres's Definition of Basis for a Topology
- Infimum is a continuous function, compact set
- Example of Hausdorff space $X$ s.t. $C_b(X)$ does not separate points?
- Hatcher question: How to Cut and Glue from Tetrahedron to Klein Bottle
- Can anybody recommend me a topology textbook?
- Why are convex polyhedral cones closed?

HINT: For each positive integer $n$ let $\mathscr{U}_n=\left\{B\left(x,\frac1n\right):x\in X\right\}$; this is an open cover of $X$, so it has a finite subcover $\mathscr{B}_n$. Consider $\mathscr{B}=\bigcup_{n\in\Bbb Z^+}\mathscr{B}_n$.

- Derivatives of the commutator of flows (or, what are those higher derivatives doing in my tangent space?!)
- What is the value of $\prod_{i=1}^\infty 1-\frac{1}{2^i}$?
- Count subsets of an i-set in two ways
- Strange combinatorial identity $\sum_{k=0}^{n}(-1)^{k}\binom{n}{k}\binom{2n-2k}{n-1}=0$
- Proof of “every convex function is continuous”
- Counterexample for downward monotone convergence theorem on measurable set
- $\sum_{i=1}^n i\cdot i! = (n+1)!-1$ By Induction
- Lower bounds on the number of elements in Sylow subgroups
- Prove $\gcd(a+b, a-b) = 1$ or $\gcd(a+b, a-b) = 2$ if $\gcd(a,b) = 1$
- Supremum and Infimum
- How do you formally prove that rotation is a linear transformation?
- How can I prove this monster inequality?
- On the number of countable models of complete theories of models of ZFC
- Does the exceptional Lie algebra $\mathfrak{g}_2$ arise from the isometry group of any projective space?
- Maximum value of expression: $\frac{ab+bc+cd}{a^2+b^2+c^2+d^2}$