Mandelbrot Set is Closed

Theorem

Let $M$ be the Mandelbrot set.

Then $M$ is closed in the complex plane $\C$.

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Mandelbrot set (B. B. Mandelbrot, 1980)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Mandelbrot set (B.B. Mandelbrot, 1980)