Path-connected space

A path-connected space is like a game where you have different places you can go to, and there is always a way to get from one place to another without jumping. For example, if you're playing in a park, you can always walk from the swings to the slide without jumping over any big obstacles.

In a path-connected space, there are different places called points, and you can think of them like little dots. You can draw lines between the dots, and these lines are called paths.

Now, if you can draw a path between any two dots, then the space is path-connected. This means that no matter where you start and where you want to end up, you can always find a path to get there without jumping over anything big.

Just like in the park, where you can always walk from the swings to the slide, in a path-connected space, you can always find a way to get from one point to another by following the paths. And that's what makes a path-connected space special!