One is a simple geometric lattice in the shape of a ring, with each node connected locally to its neighbors.

For any positive integer n, the Euclidean space is connected and locally connected.

The subspace of the real line is locally connected but not connected.

This can be used to explain the aforementioned fact that the rational numbers are not locally connected.

Similarly, they could connect to shared printers on the dedicated server, and print as if the printer was connected locally.

The topological space is usually assumed to be also a locally connected and Hausdorff space.

A space is locally connected if every point has a local base consisting of connected sets.

There also may be software-only interfaces on the router, which it treats as if they were locally connected.

The space is locally connected and path connected, while not arc connected.

It is conjectured that the Mandelbrot set is locally connected.