I need some clarification about one-point compactifications. In one of my exercise I want to show what is the space $X$ such as its compactification is $S^3\setminus\gamma$ where gamma is a circumference of $S^3$.
With my little knowledge of compactification I know that the compactification of any $\mathbb{R}^n$ is $S^n$, so I suppose that the space $X$ is $\mathbb{R}^3\setminus\delta$ where $\delta$ is a straight line in $\mathbb{R}^3$.
How can I do that?
2026-03-27 12:07:59.1774613279