There is an assumption in mathematics that if we use an adjective with a noun, it will specialize the noun, that is, it adds an additional constraint to it, yet

There is an assumption in mathematics that if we use an adjective with a noun, it will specialize the noun, that is, it adds an additional constraint to it, yet it remains to be the original noun as well. (In other words, the Liskov substitution principle holds.) It is almost always wrong. An adjective can generalize the noun, which is funny, because in that case either the adjective or the noun must be wrong. It's called the "red herring principle"[0], that is, red herrings are not red, or are not herrings. Like:[1] - a manifold with boundary is not a manifold, or it doesn't have a boundary, but can't be both - a nonassociative algebra, is either associative, or not an algebra - multivalued functions, partial functions, contravariant functors, noncommutative geometries, etc etc etc [0] : https://ncatlab.org/nlab/show/red+herring+principle https://ncatlab.org/nlab/show/red+herring+principle [1] : https://ncatlab.org/nlab/show/red+herring+principle#examples https://ncatlab.org/nlab/show/red+herring+principle#examples