Stone compactification of additive generalized-algebraic lattices
Submitted: 2013-11-18
|Accepted: 2013-11-18
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Keywords:
Additivity, Generalized way-below relation, Lower homomorphism, Upper adjoint
Supporting agencies:
Partially supported by the National Natural Science Foundation of China (Grant No. 10471035/A010104) and Natural Science Foundation of Shandong Province (Grant No. 2003ZX13).
Abstract:
In this paper, the notions of regular, completely regular, compact additive generalized algebraic lattices are introduced, and Stone compactification is constructed. The following theorem is also obtained.
Theorem: An additive generalized algebraic lattice has a Stone compactification if and only if it is regular and completely regular.
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