Let's avoid equivocating here: "the continuum" is sometimes used to refer to the real numbers, but "continuity" in this context is a property of functions between metric spaces (or possibly topological spaces). "The continuum hypothesis" and "continuous functions" are actually from completely different branches of mathematics.
This happens fairly often in mathematics, where similar-sounding terms are used to describe completely different concepts, or the same term sometimes means different things in context, or sometimes an Adjective Noun is neither described by Adjective nor by Noun.
This happens fairly often in mathematics, where similar-sounding terms are used to describe completely different concepts, or the same term sometimes means different things in context, or sometimes an Adjective Noun is neither described by Adjective nor by Noun.