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Show that the projection of a convex set $K$ on $\mathbb{R}^n$ is an interval.

I am trying to solve the following:

Let $K$ be a non-empty, convex subset of $\mathbb{R}^n$ and $f:K\to\mathbb{R}^n$ the projection defined by $f(x)=\arg\max\limits_{y\in K}\left\langle y,x\right\rangle$. Show that $f(x)=\arg\min\limits_{y\in K}\left\langle y,x\right\rangle$ for all $x\in K$.

I already know that $f$ is linear and that $f$ is non-decreasing because
$$
\arg\max\limits_{y\in K}\left\langle y,x\right\rangle=\arg\min\limits_{y\in K}\left\langle y,x\right\rangle
$$
Since $K$ is convex, every linear function of $x$ is contained in $K$. So we need to show that $\arg\max\limits_{y\in K}\left\langle y,x\right\rangle$ is a unique

I have no idea why the code isn't working. Any help would be greatly appreciated.

A:

This is because of the `` in your regular expression. You need to escape that:
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A new Toronto police report released on Monday says an officer investigating a report of a suspicious death at a house on Queen Street West in the city's west end should have remained inside, a finding that the police chief says could have "eliminated the possibility" the bullet could have lodged in her head.

The report says Toronto police were called to the house after seeing two men on fire in the backyard on April 15, 2018.

The officer involved has since been the subject of five complaints with Toronto police's professional standards division.

What officers say they did wrong

An additional 14 complainants have also lodged complaints against the officer, alleging that she had failed to properly investigate a case that could have had a "powerful" effect on the city's homicide rate.

The officer was outside when she heard the first shots and they were outside for a period of time. — Const. Craig Brister of Toronto police

Other officers who responded to the incident said that they "may have done things differently," according to the report.

One officer said that while on scene, he believed he heard two shots coming from the backyard and moved inside the home to investigate while another officer went outside.

Another officer went inside the home while several detectives remained outside as backup.

Toronto police Chief Mark Saunders said that after reviewing the report, he "really questions" whether an officer should have remained outside while investigating a call that sparked a serious response and one where several detectives were on scene.

"If I'm a rookie and I get told to stay outside, I will stay outside," Saunders said on Monday.

"When I say stay outside, I mean stay outside. You're not going inside. Don't go inside. Stay outside. You don't go in, you're done. There was no reason to be in there, why would you go in there?"

In a statement, Toronto police spokesperson Meaghan Gray said that police "have reviewed the report and, given what is known at this time,
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