On the continuity of lattice isomorphisms on C(X, I)
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Vahid Ehsani
Abstract
We investigate topological conditions on a compact Hausdorff space Y, such that any lattice isomorphism φ : C(X, I) → C(Y, I), where X is a compact Hausdorff space and I is the unit interval [0, 1], is continuous. It is shown that in either of cases that the set of Gδ points of Y has a dense pseudocompact subset or Y does not contain the Stone-Čech compactification of ℕ, such a lattice isomorphism is a homeomorphism.
(Communicated by Marcus Waurick)
Acknowledgement
The authors would like to thank the referees for their invaluable comments to improve the paper.
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- Regular Papers
- Semidistributivity and Whitman Property in implication zroupoids
- Composition of binary quadratic forms over number fields
- On Z-Symmetric Rings
- On the factorable spaces of absolutely p-summable, null, convergent, and bounded sequences
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- Existence of traveling wave solutions in nonlocal delayed higher-dimensional lattice systems with quasi-monotone nonlinearities
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