# Neighborhood

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, (c) 1987-2023.

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