Converses of Bishop's lemma on located sets (Q5935882)

The paper proves partial converses of Bishop's Lemma on complete located subsets of a metric space. The proof is carried out within the frame of Bishop's constructive mathematics. The constructive notions of uniformly almost located and continuously reflective are introduced and used. A Brouwerian example is provided to show that one cannot remove the hypothesis of local total boundedness from Theorem 1 and the hypothesis of finite-dimensionality from Proposition 5.