# Partitions of unity in constructive mathematics

Can someone point me to any substitutes for the partition of unity in Bishop's constructive mathematics?

In particular, under what circumstances can we construct a partition of unity subordinate to some open cover of a compact set in Euclidean space?

• Can your result be related to complete regularity (every open set is the inverse image of $(0, 1)$)? – Andrej Bauer Jun 25 '18 at 19:03