Infinite-dimensional Lie groups without completeness restrictions

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Differentiable mappings on products with different degrees of differentiability in the two factors (2012, methodology): “We study such mappings in an infinite-dimensional setting, which is analogous to the approach to C-maps between locally convex spaces known as Keller’s C c -theory [25] (see [30], [24], [31], [13] and [23] for streamlined expositions, cf.”
Algebras whose groups of units are Lie groups (2002, background): “See [13] for a detailed exposition of the slightly generalized setting.”
Differential Calculus over General Base Fields and Rings (2004, methodology): “However, all of the basic theory (as described on a few pages in [26], Section 1) is easily seen to work just as well for non-locally convex E, and also over the complex field (by trivial adaptations of the proofs); all which matters is the local convexity of the range F.”
Fundamentals of direct limit Lie theory (2004, background): “Maps and manifolds which are holomorphic in the convenient sense will be called c∞ C or cω C .”
Implicit functions from topological vector spaces to Banach spaces (2003, background): “j+1 R (cf. [ 10 ]). Thus, the assertions of the theorem hold in situation (i).”