Topological groups, which integrate algebraic group structures with continuous topologies, and metric spaces, defined by a distance function, form a fundamental basis for modern mathematical analysis.

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 ...

In recent years, physicists have been trying to better understand the behavior of individual quantum particles as they move in space. Yet directly imaging these particles with high precision has so ...

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 ...