Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
This answers a previous variant of the question above:
Suppose that $V_1=\mathbb{R}^2$ with standard Euclidean metric, and $V_2=\mathbb{R}$. Let $\pi(x,y)=x+2y$. Then $\pi(\Sigma_1)$ contains both $1$ and $2$.
Suppose that $V_1=\mathbb{R}^2$ with standard Euclidean metric, and $V_2=\mathbb{R}$. Let $\pi(x,y)=x+2y$. Then $\pi(\Sigma_1)$ contains both $1$ and $2$.
This answers a previous variant of the question above:
Suppose that $V_1=\mathbb{R}^2$ with standard Euclidean metric, and $V_2=\mathbb{R}$. Let $\pi(x,y)=x+2y$. Then $\pi(\Sigma_1)$ contains both $1$ and $2$.
Suppose that $V_1=\mathbb{R}^2$ with standard Euclidean metric, and $V_2=\mathbb{R}$. Let $\pi(x,y)=x+2y$. Then $\pi(\Sigma_1)$ contains both $1$ and $2$.
