Earlier quoted context omitted.
I'm aware that "locally connected" has a very specific meaning in math: https://en.wikipedia.org/wiki/Locally_connected_space Unfortunately I don't have the slightest idea what it actually means... that article does not have any ELI5 sentence within it.
>Unfortunately I don't have the slightest idea what it actually means Not just me then? ;0)
"MLC posits that the Mandelbrot set isn’t just connected; it’s locally connected — no matter how much you zoom in on the Mandelbrot set, it will always look like one connected piece. For instance, a circle is locally connected. An extremely fine-toothed comb, on the other hand, is not. Though the entire shape is connected, if you skip over the shaft and instead zoom in on the tips of some of its teeth, you’ll just see a bunch of separate line segments."