Direct limit Lie groups and manifolds

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Fundamentals of direct limit Lie theory (2004, background): “Received 1 August 2004, accepted in final form 1 October 2004.”
Final group topologies, Kac-Moody groups and Pontryagin duality (2006, background): “Furthermore, if C is a proper subgroup of ers more complicated diagrams of topological groups and their colimits (e.g., colimits of amalgams of more than two factors).”
On Differentiable Vectors for Representations of Infinite Dimensional Lie Groups (2010, background): “If (Gn)n∈N is a sequence of finite dimensional Lie groups with homomorphisms φn : Gn → Gn+1, then Glöckner has shown in [11] that the corresponding direct limit group G := lim −→ Gn, endowed with the direct limit topology carries a compatible Lie group structure with Lie algebra g := lim −→ L(Gn), e”