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This theory builds on Bolzano's view (1851), which in turn is mirrored by the standard account of point-set topology.
Indeed, it turns out that inductive complexity can be captured in terms of point-set topology and corresponds to a scale of topological complexity that has much importance in mathematics (the Borel and finite-difference hierarchies [Kelly 1996]).
For the purposes of this article, "analysis" will be limited to the generalization and extension of the concepts of calculus, using the concepts of elementary point-set topology.