I'm going to build the foundations of topology, continuity and the like in terms of sub-relations of the relation `sub-relation'. First, however, I'd better expand my brief discussion of sub-relations in my introduction to relations.

A relation s is a sub-relation of a relation r precisely if `s relates x to y' implies `r relates x to y'. This makes `is a sub-relation of' a relation whose initial and final values are all relations.

Written by Eddy.
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