On exposed semigroup homomophins
Tóm tắt
In the main theorem of this paper the existence of weakly exposed semigroup homomorphisms is proved. This theorem is effectively equivalent to the axiom of choice and generalizes some well known theorems of functional analysis like the Hahn-Banach theorem, the Krein-Milman theorem, Bauer's minimum principle and a result of T. Husain and I. Tweddle.
Tài liệu tham khảo
Alfsen, E.M., Compact convex Sets and Boundary Integrals, Springer-Verlag, Berlin-Heidelberg New York (1971).
Bell, J.L. and D.H. Fremlin, A geometric form of the axiom of choice, Fundamenta Mathematica 77 (1972), 167–170.
Fuchssteiner, B., Sandwich theorems and lattice semigroups, J. Functional Analysis 1 (1974), 1–14.
Husain, T. and I. Tweddle, On the extreme points of the sum of two compact convex sets, Math. Ann. 188 (1970) 113–122.
Luxemburg, W.A.J., Math. Reviews 43 (1972) # 7879
Schaefer, H.H., Banach Lattices and positive Operators, Springer-Verlag, Berlin-Heidelberg-New York (1974)