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Note if any point is contained in some smaller version of the whole, then any point is contained in arbitrarily smaller versions of the whole.
It isn't possible to unambiguously communicate in a picture whether or not a few specific points are included in the fractal. The pictures are interpreted as what is intuitively simplest. To make matters less ambiguous, all the fractals here contain all points arbitrarily close to points in them. (They are topologically closed. See also BP1239.)
The left hand side of this is a stronger condition than the left hand side of BP1116. | 
