Intereting Posts

Distribution of $(XY)^Z$ for $(X,Y,Z)$ i.i.d. uniform on $(0,1)$
Intuition behind Cantor-Bernstein-Schröder
Double Factorial: Number of possibilities to partition a set of $2n$ items into $n$ pairs
Which spheres are fiber bundles?
Good book for high school algebra
Why isn't $f(x) = x\cos\frac{\pi}{x}$ differentiable at $x=0$, and how do we foresee it?
Describe the structure of factor ring $\mathbb{Z}/(2+\sqrt{5})$.
How to reduce higher order linear ODE to a system of first order ODE?
Are there prime gaps of every size?
Solution of the integral equation $y(x)+\int_{0}^{x}(x-s)y(s)ds=x^3/6$
Galois group of $x^4-5$
Proof that plane with $N$ lines can be painted with two colors so that any two neighboring regions are painted in different colors
Bounded sequence which is not convergent, but differences of consecutive terms converge to zero
Non-constructive proof that $\sum_{j=1}^n j^k$ is a polynomial $p(n)$ of degree $k+1$
If $A$ is the generator of $(P_t)$, then $A+f$ is the generator of $(P_t^f)$

Let $E$ be a $T_1$ space, and $A\subset E$ , I need to prove that $A’$ is closed, so my idea is to prove that $C_{E}A’$ is open i.e a neighborhood of all it’s point.

But how to do this ?

- Compactness of unit ball in WOT of B(X)
- Help needed with last step in proof of Tychonoff theorem
- Euler characteristic of a quotient space
- What are the epimorphisms in the category of Hausdorff spaces?
- Perfect set without rational numbers
- Compact Hausdorff spaces w.o isolated points and having countable bases consisting of clopen sets are homeomorphic?

- Basic facts about ultrafilters and convergence of a sequence along an ultrafilter
- Does factor-wise continuity imply continuity?
- Free cocompact action of discrete group gives a covering map
- separation properties in Hausdorff, compact spaces
- Example of Hausdorff and Second Countable Space that is Not Metrizable
- Proving that if a set is both open and closed then it is equal to the real numbers
- Classification Theorem for Non-Compact 2-Manifolds? 2-Manifolds With Boundary?
- Smooth structure on the topological space
- Arcwise connected part of $\mathbb R^2$
- Why did we define the concept of continuity originally, and why it is defined the way it is?

HINT: If $x\in E\setminus A’$, then $x$ has an open nbhd $U_x$ such that $U_x\cap A$ contains at most one point. Show that $U_x\cap A’=\varnothing$.

- Is there a recommended symbol for “equal by abuse of notation”?
- Are logarithms of prime numbers algebraically independent?
- What are the zero divisors of $C$?
- Criterion for being a simple group
- Cartesian product of dense sets is dense?
- When can stalks be glued to recover a sheaf?
- If $x^4 \equiv -1 \mod p$ then $p \equiv 1 \mod 8$
- Flip a coin until a head comes up. Why is “infinitely many tails” an event we need to consider?
- Expectation of a discrete random variable: how to convert an integral to a sum?
- Map closed under addition but not multiplication
- The case of Captain America's shield: a variation of Alhazen's Billard problem
- Show that the sum $\frac {1}{p_1} + \frac {1}{p_2} +\frac {1}{p_3} +…+\frac {1}{p_n}$ is never an integer,where $p_i$'s are primes,$ 1\le i \le n$.
- Free groups and relations. Showing that $G\simeq FG^{(3)}/N$ for $N$ the normal subgroup generated by a set of relations.
- Determining k: $\int_{6}^{16} \frac{dx}{\sqrt{x^3 + 7x^2 + 8x – 16}} = \frac{\pi}{k}$
- Trying to solve the equation $\sum_{i=0}^{t}(-1)^i\binom{m}{i}\binom{n-m}{t-i}=0 $ for non-negative integers $m,n,t$