The example is from Munkres Topology section 23. What are the limit points of these two sets (graphs)?
2026-04-03 08:07:52.1775203672
Two indicated sets (graphs) form a separation of $X$ because neither contains a limit point of the other
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Every point in the graphs are the limit points, and only those points are the limit points. Since the graphs do not cross, neither contains a limit point of the other.