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This theory builds on Bolzano's view (1851), which in turn is mirrored by the standard account of pointset topology.

Indeed, it turns out that inductive complexity can be captured in terms of pointset topology and corresponds to a scale of topological complexity that has much importance in mathematics (the Borel and finitedifference 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 pointset topology.
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