In the march of development of my theory, I have expressed many kinds of spaces (topological, proximity, uniform spaces, etc.) through funcoids and reloids subsuming their properties (such as continuity) for my algebraic operations.

Now I have expressed Cauchy spaces (and some more general kinds of spaces) through reloids. And yes, Cauchy continuity appears as a special case of continuous reloids (as expressed by my algebraic formulas).

My research related with Cauchy spaces is presented in this draft article.

Read my book before.