We present a notion of precompactness, and study some of its properties, in the context of apartness spaces whose apartness structure is not necessarily induced by any uniform one. The presentation lies entirely with a Bishop-style constructive framework, and is a contribution to the ongoing development of the constructive theories of apartness and uniformity.

• 03F60 - Constructive and recursive analysis
• 54E05 - Proximity structures and generalizations
• 54E15 - Uniform structures and generalizations