A [matrix Lie group](Matrix%20Lie%20group.md), $\mbox{G}$ is said to be [[Simply connected]] if it is a [connected group](Connected%20topological%20groups.md) and in addition, * For every [continuous](Continuity.md) path $A(t)$ along $0\leq t \leq 1$ lying in $\mbox{G}$ where $A(0)=A(1)$ there exists a continuous function $A(s,t)$ where $s\geq 0$ in $\mbox{G}$. * The following properties of $A(s,t)$ are met: 1) $A(s,0)=A(s,1)\;\forall s.$ 2) $A(0,t)=A(t).$ 3) $A(1,t)=A(1,0)\;\forall t$ #MathematicalFoundations/Algebra/AbstractAlgebra/GroupTheory/Lie/LieGroups/Algebras/LieAlgebras #MathematicalFoundations/Geometry/Topology