The Stacks project

Example 26.19.6. An open immersion is in general not quasi-compact. The standard example of this is the open subspace $U \subset X$, where $X = \mathop{\mathrm{Spec}}(k[x_1, x_2, x_3, \ldots ])$, where $U$ is $X \setminus \{ 0\}$, and where $0$ is the point of $X$ corresponding to the maximal ideal $(x_1, x_2, x_3, \ldots )$.