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Colorimetry is based upon an equivalence relation ∼ (s, t), for s, t ∈ S.
When ∼ (s, t) then “s and t are indiscriminable”. Typically
¬ ∼ (s, t), thus indiscriminability is very special.
“Color space” C is defined as C = S/ ∼. Its elements (“colors”)
are equivalence sets of ∞ cardinality.
∼ (s, t) doesn’t imply s = t, but s−t ∈ K or ∼ (s−t, ∅), where ∅
is the “empty beam”. The linear space K is the “black space”.
Thus “Color Space” is the Space of Beams with the Black Space
collapsed to zero: C = S/K.
Empirically one finds dim C = 3 for generic human observers. All
colors are projections from S + . They form a convex cone C + ⊂ C.
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