In topology, a topological space is called simply connected if it is path-connected and every path between two points can be continuously transformed into any other such path while preserving the two endpoints in question.

What does it mean for a set to be simply connected?

A simply connected domain is a path-connected domain where one can continuously shrink any simple closed curve into a point while remaining in the domain. For two-dimensional regions, a simply connected domain is one without holes in it. ... A simply connected domain is one without holes going all the way through it.

What is the difference between connected and simply connected?

It is a classic and elementary exercise in topology to show that, if a space is path-connected, then it is connected. Thus, if a space is simply connected, then it is connected.