scholarly journals A constructive Galois connection between closure and interior

2012 ◽  
Vol 77 (4) ◽  
pp. 1308-1324 ◽  
Author(s):  
Francesco Ciraulo ◽  
Giovanni Sambin
Keyword(s):  
Galois Connection ◽  
Classical Correspondence ◽  
Intuitionistic Version

AbstractWe construct a Galois connection between closure and interior operators on a given set. All arguments are intuitionistically valid. Our construction is an intuitionistic version of the classical correspondence between closure and interior operators via complement.

scholarly journals Complexity of quantum motion and quantum-classical correspondence: A phase-space approach

2020 ◽  
Vol 2 (4) ◽  
Author(s):  
Jiaozi Wang ◽  
Giuliano Benenti ◽  
Giulio Casati ◽  
Wen-ge Wang
Keyword(s):  
Phase Space ◽  
Classical Correspondence ◽  
Quantum Motion ◽  
Space Approach

scholarly journals Classical correspondence of quantum entanglement in mesoscopic circuit

2022 ◽  
Vol 71 (1) ◽  
pp. 1-7
Author(s):  
Fan Hong-yi ◽  
◽  
Wu Ze ◽  
Keyword(s):  
Quantum Entanglement ◽  
Classical Correspondence

scholarly journals ON THE PARTITION MONOID AND SOME RELATED SEMIGROUPS

2010 ◽  
Vol 83 (2) ◽  
pp. 273-288 ◽  
Author(s):  
D. G. FITZGERALD ◽  
KWOK WAI LAU
Keyword(s):  
Transformation Semigroup ◽  
Galois Connection ◽  
Inverse Semigroups ◽  
Natural Order ◽  
Binary Relations ◽  
Ideal Lattices ◽  
New Interpretation ◽  
Semigroup Of Transformations ◽  
The Ideal

AbstractThe partition monoid is a salient natural example of a *-regular semigroup. We find a Galois connection between elements of the partition monoid and binary relations, and use it to show that the partition monoid contains copies of the semigroup of transformations and the symmetric and dual-symmetric inverse semigroups on the underlying set. We characterize the divisibility preorders and the natural order on the (straight) partition monoid, using certain graphical structures associated with each element. This gives a simpler characterization of Green’s relations. We also derive a new interpretation of the natural order on the transformation semigroup. The results are also used to describe the ideal lattices of the straight and twisted partition monoids and the Brauer monoid.

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