Turkish Journal of Mathematics
Abstract
Let X and Y be compact Hausdorff spaces with Y hyperstonean. In this paper, we prove that if C(X,R) and C(Y,R) are lattice isomorphic then these Banach spaces are linearly isometric, and, consequently, X and Y are homeomorphic, which in turn implies that X is also hyperstonean. Actually, we prove more than what is announced in the headline above. This result, in some ways, is a generalization of the well-known Banach-Stone theorem.
DOI
10.55730/1300-0098.3488
Keywords
Hyperstonean space, Banach-Stone theorem, lattice isomorphism
First Page
15
Last Page
20
Recommended Citation
GÜNTÜRK, B (2024). On the invariance of hyperstoneanness under lattice isomorphisms. Turkish Journal of Mathematics 48 (1): 15-20. https://doi.org/10.55730/1300-0098.3488
