Path-connected

When we say a space is path-connected, it means that we can connect any two points in the space with a line or a path. Think of it like drawing a line from one point to another on a piece of paper. If we can draw that line without lifting our pen or going off the paper, then the space is path-connected.

For example, if we have a circle, we can draw a path from any point on the circle to any other point on the circle without lifting our pen or going off the circle. Therefore, we say the circle is path-connected.

However, if we have two separate circles that aren't touching, we can't draw a path from a point on one circle to a point on the other circle without lifting our pen or going off the circles. Therefore, we say the two circles together are not path-connected.

In summary, a space is path-connected if we can draw a line or path connecting any two points in that space without lifting our pen or going off the space.