The first part of the paper introduces the varieties of modem constructive mathematics, concentrating on Bishop's constructive mathematics (BISH). It gives a sketch of both Myhill's axiomatic system… (More)

exists (is computable) for each x in H; if P is that projection, / is the identity operator on H, and the adjoint T*ofT exists, then / P is the projection of H on ker(3*), the kernel of T*. (For an… (More)

Our discussion takes place in the context of Bishop’s constructive mathematics (BISH; [3, 4]), in which “existence” is interpreted strictly as “constructibility.”3 One distinctive feature of BISH,… (More)

The paper opens with a discussion of the distinction between the classical and the constructive notions of "computable function." There then follows a description of the three main varieties of… (More)

We examine, within the framework of Bishop's constructive mathematics, various classical methods for proving the existence of weak solutions of the Dirichlet Problem, with a view to showing why those… (More)

A notion of Cauchy net is introduced into the constructive theory of apartness spaces. It is shown that for a sequence in a metric space this notion is equivalent to the standard metric notion of… (More)

The relations among a set, its complement, and its boundary are examined constructively. A crucial tool is a theorem that allows the construction of a point where a segment comes close to the… (More)

A first—order axiomatic constructive development of the theory of nearness and apartness of a point and a set is introduced as a setting for constructive topology.

Two weakenings of the anti-Specker property—a principle of some significance in constructive reverse mathematics—are introduced, examined, and in one case applied, within Bishop-style constructive… (More)