ABSTRACT
Let X be a compact Hausdorff space, A a (real or complex) subalgebra of (real or complex) C(X) containing the constants. Call K ⊂ X a set of antisymmetry of A or an A-antisymmetric set if f ∈ A and f real on K implies f constant on K (i.e., g, g ¯ ∈ A | K https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072645/d0c716e9-d02e-4ae2-8880-b8eca47a1243/content/eq47.tif"/> implies g constant). Call A an antisymmetric algebra if X is an A-antisymmetric set, that is, if A contains no non-constant real functions.
