The uniform boundedness theorem and a boundedness principle

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Abstract

We deal with a form of the uniform boundedness theorem (or the Banach–Steinhaus theorem) for topological vector spaces in Bishop’s constructive mathematics, and show that the form is equivalent to the boundedness principle BD-N, and hence holds not only in classical mathematics but also in intuitionistic mathematics and in constructive recursive mathematics. The result is also a result in constructive reverse mathematics.

MSC

03F60
46S30

Keywords

Constructive mathematics
Topological vector space
The uniform boundedness theorem
Boundedness principle

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