File talk:Accumulation And Boundary Points Of S.PNG

Wrong?
This image, or at least its caption in Boundary (topology) is wrong, isn't it? At the very least, the first obvious problem I notice is that every point in S should belong to either its interior or to its boundary. And I believe accumulation points should also belong in the closure (union of interior and boundary), although our article on them is somewhat confusing.

I'm not sure how to fix this; probably the best way would be to draw a whole new diagram from scratch. Maybe just something simple showing the interior, boundary and exterior. Stuffing the isolated and accumulation points into the same diagram makes it rather complex. —Ilmari Karonen (talk) 23:31, 24 November 2006 (UTC)