🚀 go-pugleaf

Some time back, someone (whose name and article I've forgotten)
inquired as to whether, since the Mandelbrot set is connected, its
boundary couldn't be shown to be a simple (but nasty) closed curve in
the complex line C.  A response was given in the group, pointing to
current research along that line (and indicating that the question was
still open).  I have nothing new to add to that, only to suppose that
those interested in this issue were aware of the following property
that uniquely characterizes the circle S^1 (and thus would suffice to
determine whether the boundary of the Mandelbrot set is in fact such a
beast):

	The circle is the unique topological space for which:

		1) no single point separates the space

	and

		2) every pair of distinct points does separate the
		   space. 

Here, a set separates a space if its complement is not connected. (so,
for instance, the empty set separates any non-connected space).

Just an observation that might be of some value.

						Dale.