====== MLC conjecture ======

The MLC Conjecture - //Mandelbrot Locally Connected// - suggests that the fractal, known as the [[https://en.wikipedia.org/wiki/Mandelbrot_set|Mandelbrot Set]] is 'locally connected'.

'Locally Connected' in this instance is defined thus :

>A topological space is locally connected at the point {{https://mathworld.wolfram.com/images/equations/LocallyConnected/Inline1.gif?7x15|x}} if every neighborhood of {{https://mathworld.wolfram.com/images/equations/LocallyConnected/Inline2.gif?7x15|x}} contains a connected open neighborhood. It is called locally connected if it is locally connected at every point."
> \\ Source [[https://mathworld.wolfram.com/LocallyConnected.html|Wolfram Mathworld]]

The conjecture remains 'open' - i.e has neither been proved or disproved.

See [[https://en.wikipedia.org/wiki/Mandelbrot_set#Local_connectivity|Wikipedia]]