 Facebook Friend Mapper Extension: Browsing through Facebookâ€™s app store is not one of my most favorite things to do, butÂ . Extension – Facebook. 2 days ago – This extension lets you see any Facebook friend’s hidden friends list, which is a greatÂ .Q: Projection of a manifold on a codimension one subspace Define a map $f\colon M\rightarrow\mathbb{R}^{n}$ to be a local embedding if for any compact subset $K\subset M$, there is an open set $U$ such that $f|_{K}$ is an embedding. This is a very important condition in differential geometry and many differential topological notions are invariant under local embedding. However, it is also easy to see that the condition is too strong as there are many non-local embeddings. Let $f\colon M\rightarrow \mathbb{R}^{n}$ be a smooth map and let $W=\{w_{1},\dots,w_{k}\}$ be any basis for $V$ and $K=\cup_{j=1}^{k}B_{\epsilon}(w_{j})\subset \mathbb{R}^{n}$, where $B_{\epsilon}(w_{j})$ is the open ball centered at $w_{j}$ with radius $\epsilon$. Then $f^{ -1}(K)$ is a closed subset of $M$, so $f$ is not a local embedding. But it is easy to see that $f$ is a local embedding if and only if there exists a map $g\colon M\rightarrow\mathbb{R}^{k}$ such that $g(x)=\{g_{1}(x),\dots,g_{k}(x)\}$ where each $g_{j}$ is a map from $M$ to $S^{n-1}$ such that $f|_{U}=g|_{U}$, where $U$ is the domain of all $g_{j}$. I tried to find a counterexample to show that $g$ is not a local embedding. I know that there is a local embedding from \$S^{n} 50b96ab0b6