Incidence algebras as algebras of endomorphisms
William H. Graves, Suzanne M. Molnar · Bulletin of the American Mathematical Society · 1973
PROPOSITION 2. This topology on M(P) is discrete if and only ifP is lower finite.PROOF.This topology on M(P) is discrete if and only if {0} e 31 if and only if 0 is a (*)-set if and only if P is lower finite.PROPOSITION 3.This topology on M(P) is Hausdorff.PROOF.For xeP, let S x = P -{x}.Then S x is a.(*)-set, and f]N(S x ) = {0}.