galois connection造句

• The Galois connection is not uniquely determined by the closure operator.
• For example, ( monotone ) Galois connections have this property.
• The literature contains two closely related notions of " Galois connection ".
• Applying the basic property of Galois connections, one can now conclude that.
• Therefore, the notions of monotone Galois connection and residuated mapping essentially coincide.
• The antitone Galois connections do not share this property.
• The notion of closure is generalized by Galois connection, and further by monads.
• Therefore, the notion of residuated mapping and monotone Galois connection are essentially the same.
• However, mentioning monotonicity helps to avoid confusion about the two alternative notions of Galois connections.
• Dilations and erosions form Galois connections.
• Hence, considering complete lattices with complete semilattice morphisms boils down to considering Galois connections as morphisms.
• In this situation, an important feature of Galois connections is that one adjoint uniquely determines the other.
• The orthogonal complement is thus a Galois connection on the partial order of subspaces of a Hilbert space.
• All of the below statements on Galois connections can thus easily be converted into statements about antitone Galois connections.
• All of the below statements on Galois connections can thus easily be converted into statements about antitone Galois connections.
• In fact, " every " closure operator arises in this way from a suitable Galois connection.
• Any Galois connection gives rise to closure operators and to inverse order-preserving bijections between the corresponding closed elements.
• The reason is that, being the lower adjoint of a Galois connection, \ wedge preserves all existing suprema.
• A more elaborate type of functions is given by so-called "'Galois connections " '.
• On the other hand, we can conclude that every such mapping is the lower adjoint of some Galois connection.