happens,
and this is a very common tactic in mathematical practice,
it is very useful to begin by weakening it, and simply to
incorporate all subsets of such a space under a "nominal"
title of sign relations, only coming back at the second
or third pass to note that some of them qualify only in
a "trivial" way.  The properties that they have are the
properties that they have.  It is our job but to notice,
to describe, and to articulate them, species by species,
genus by genus, an so on.  It is all very stra