By definition, if $A$ is simply-connected then $A$ is connected.
I would like to know why in the Wikipedia we find this phrase: "The Heisenberg group is a connected, simply-connected Lie group ...", because it is sufficient to say "The Heisenberg group is a simply-connected Lie group ..." only.
My problem is, why connected and simply-connected (both at the same time), it is sufficient to write just simply-connected.
Thank you in advance
Simply connected means that any closed curve is homotopic to the constant curve. If you take two copies of a simply connected space - for example two disjoint points - they are still simply connected, but not connected.