Complex Analysis on Infinite Dimensional Spaces

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The study of infinite dimensional holomorphy explores holomorphic functions in complex topological vector spaces, intertwining various mathematical disciplines such as topology, complex variables, and functional analysis. It emphasizes the interconnectedness of these fields and the evolution of mathematical thought over decades. The author reflects on the challenges of selecting topics for a course, highlighting two distinct approaches: the geometric-algebraic theory linked to bounded symmetric domains and the topological theory, which is the focus of this work.