Functional data analysis is typically conducted within the L²-Hilbert space framework. There is by now a fully developed statistical toolbox allowing for the principled application of the functional ...

Continuation of APPM 4440. Study of multidimensional analysis including n-dimensional Euclidean space, continuity and uniform continuity of functions of several variables, differentiation, linear and ...

Topological spaces form the foundational framework for modern analysis and geometry, characterised by a set equipped with a collection of open subsets satisfying specific axioms. This flexible ...

We give a systematic technical exposition of the foundations of the theory of computably compact metric spaces. We discover several new characterizations of computable compactness and apply these ...