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In $L^p(\mathbb R)$ or $\ell^p$ for $1 \le p \le \infty$,, $\{f: |f(x)| \le |x| \}$$\{f: 0 < f(x) \le |x| \ \text{for}\ x \ne 0 \}$.
In $L^p(\mathbb R)$ or $\ell^p$ for $1 \le p \le \infty$,, $\{f: |f(x)| \le |x| \}$.
In $L^p(\mathbb R)$ or $\ell^p$ for $1 \le p \le \infty$, $\{f: 0 < f(x) \le |x| \ \text{for}\ x \ne 0 \}$.
