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Explore the fundamental connections between reverse mathematics and mathematical analysis in this lecture from the Summer School on "Reverse Mathematics: New Paradigms." Begin by reviewing the "big five" subsystems of second-order arithmetic and their essential properties, then establish rigorous definitions of open and closed sets alongside continuous functions within Polish spaces. Delve into the reverse mathematical foundations of basic analysis, examining how various analytical concepts relate to different subsystems of second-order arithmetic. Investigate extended definitions of functions on Polish spaces and discover additional analytical topics through the lens of reverse mathematics, gaining insight into the logical strength required for fundamental theorems in analysis.
