Ultrametric and non-locally convex analogues of the general curve lemma of convenient differential calculus

The General Curve Lemma is a tool of Infinite-Dimensional Analysis, which enables refined studies of differentiability properties of mappings between real locally convex spaces. In this article, we generalize the General Curve Lemma in two ways: First, we remove the condition of local convexity in the real case. Second, we adapt the lemma to the case of curves in topological vector spaces over ultrametric fields.