Locally path-connected space

Imagine you are playing with building blocks. Each block represents a point in a space. Now, let’s say you can connect any two neighboring blocks with a string. This creates a path between those two blocks.

A space is locally path-connected if there is a path between any two neighboring blocks or points. This means that if you start at one block, and move to a block right next to it, you can connect those two blocks with a path.

Think about it as if you are trying to jump from one block to another, but there is a string tying them together. This makes it easy to move around the space you are in.

So, if a space is locally path-connected, you can easily move around it without getting stuck in one place.