Quasi-uniform spaces IV: Formal balls—a proposal

Formal balls are an extraordinarily useful notion in the study of quasi-metric, and even hemi-metric spaces. Is there any way of extending the notion to the case of quasi-uniform spaces? This is what I would like to start investigating. This is pretty experimental, and I don’t make any guarantee that any of what I am going to say leads to anything of any interest whatsoever! Read the full post.