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.
From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2017. Mu-ency index
This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2017 Feb 02. s.11