Intereting Posts

Logic: Using Quantifiers To Express “At Least 2?”
Why is Volume^2 at most product of the 3 projections?
A conditional normal rv sequence, does the mean converges in probability
If $A \in M_{n \times 1} (\mathbb K)$, then $AA^t$ is diagonalizable.
Why have we chosen our number system to be decimal (base 10)?
Homeomorphism between the Unit Disc and Complex Plane
How can I prove $\lim_{n \to \infty} \int_{0}^{\pi/2} f(x) \sin ((2n+1) x) dx =0 $?
Making Tychonoff Corkscrew in Counterexamples in Topology rigorous?
Simple module and homomorphisms
Taking the second derivative of a parametric curve
Evaluating $\int_0^{\infty} {\frac{\sin{x}\sin{2x}\sin{3x}\cdots\sin{nx}\sin{n^2x}}{x^{n+1}}}\ dx$
Can there be a point on a Riemann surface such that every rational function is ramified at this point?
Evaluate $\lim_{x \to 0} \left(\frac{1}{\ln(1+x)} + \frac{1}{\ln(1-x)}\right)$
What's wrong with this argument? (Limits)
Field Norm Surjective for Finite Extensions of $\mathbb{F}_{p^k}$

I’m trying to understand the CW complex structure of the projective space $\mathbb{RP}^n$, but some things are unclear. I understand we start by identifying $\mathbb{RP}^n$ with $S^n/R$ where $R$ is the equivalence relation identifying antipodal points on the sphere. This is fine. But then $S^n/R$ is identified to $D^n/R$ with R this time restricted to the border $S^{n-1}$ of $D^n$. Here is my problem: can anybody provide an explicit map of this identification? And secondly, how can we identify this last space to the adjoint space of $\mathbb{RP}^{n-1}$ and $D^n$, in other words, how does $\mathbb{RP}^{n-1}$ becomes a (n-1) skeleton of the CW-complex from here?

- Is there a “geometric” interpretation of inert primes?
- What are cohomology rings good for?
- How much of an $n$-dimensional manifold can we embed into $\mathbb{R}^n$?
- Singular $\simeq$ Cellular homology?
- how to compute the de Rham cohomology of the punctured plane just by Calculus?
- Books on topology and geometry of Grassmannians
- General relationship between braid groups and mapping class groups
- composition of certain covering maps
- Sheaf cohomology: what is it and where can I learn it?
- If $M$ is a nonorientable $3$-manifold, why is $H_1(M, \mathbb{Z})$ infinite?

The natural inclusion of the hemisphere $D^n \to S^n$ respects the relation $R$ as described. So, it induces a map $D^n/R \to S^n/R$, which is a homeomorphism. Now, consider the inclusion of the boundary $S^{n-1} \to D^n$, and see that this too respects the relation $R$, thus inducing an inclusion map $S^{n-1}/R = \mathbb R P^{n-1} \to D^n/R \cong \mathbb RP^n$. It should now be easy to see that we obtain $D^n/R \cong \mathbb RP^n$ from $\mathbb R P^{n-1}$ by attaching $D^n$ along the quotient map $S^{n-1} \to S^{n-1}/R = \mathbb RP^{n-1}$.

First see the CW-structure of $S^n$ as 2 0-cells,2 1-cells, … , 2 n-cells and attaching maps are natural.Then see that $Z/2$ act on $S^n$ by antipodal action and this $Z/2$ action flip each 2 $i$-cells.Note $RP^n = S^n / Z/2$ This gives the CW complex structure of $RP^n$.

- How to find the maximum value for the given $xcos{\lambda}+ysin{\lambda}$?
- $M$ be a finitely generated module over commutative unital ring $R$ , $N,P$ submodules , $P\subseteq N \subseteq M$ and $M\cong P$ , is $M\cong N$?
- Calculating the Modular Multiplicative Inverse without all those strange looking symbols
- Prove that a continuous function on a closed interval attains a maximum
- What's application of Bernstein Set?
- Fibonacci combinatorial identity: $F_{2n} = {n \choose 0} F_0 + {n\choose 1} F_1 + … {n\choose n} F_n$
- Prove $\mathbb{P}(\sup_{t \geq 0} M_t > x \mid \mathcal{F}_0)= 1 \wedge \frac{M_0}{x}$ for a martingale $(M_t)_{t \geq 0}$
- Expected area of the intersection of two circles
- Closed set as a countable intersection of open sets
- How to evaluate $ \int_0^\infty {1 \over x^x}dx$ in terms of summation of series?
- Number of terms in the expansion of $\left(1+\frac{1}{x}+\frac{1}{x^2}\right)^n$
- Linear dependence of linear functionals
- Working with binomial coefficient $\sum_{k=0}^n (-1)^k \binom nk=0$
- Solving the differential equation $(x^2-y^2)y' – 2xy = 0$.
- Let $f (z) $ be an entire function such that $|f (z)|≤K|z|$, $∀z∈\mathbb{C}$, for some $K>0$. If $f (1) =i$, then$f (i) $ is