analysis (differential/integral calculus, functional analysis, topology)
metric space, normed vector space
open ball, open subset, neighbourhood
convergence, limit of a sequence
compactness, sequential compactness
continuous metric space valued function on compact metric space is uniformly continuous
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constructive mathematics, realizability, computability
propositions as types, proofs as programs, computational trinitarianism
basic constructions:
strong axioms
further
Bishop 1967 introduced the principles of omniscience for the natural numbers to show that certain results in pointwise analysis could not be constructive, by showing that these results implied a principle of omniscience. There are similar axioms in analysis for various notions of real numbers which all imply the principles of omniscience for natural numbers, called the analytic principles of omniscience. These include:
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