Robert P. Munafo, 1998 Dec 29.
When working in a simple Euclidean space (like the Mandelbrot Set, which is
embedded in a plane) a neighborhood of a point is the area within a circle (or sphere, etc.) of a given radius, centered on the point in question. On the plane this is a disc.
More technically, is the space has a metric then a neighborhood is the
set of points whose metric from the given point is less than or equal to a
given value.
See also cantor set, connected, limit point.
From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo. Mu-ency index
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