galois connection造句

• This geometrizes the Galois connection at the level of finite subgroups of O ( 3 ) and PO ( 3 ), under which the adjunction is " union with central inverse ".
• Ore's early work on lattice theory led him to the study of closure relations, Galois connections, and finally to graph theory, which occupied him to the end of his life.
• A Galois connection is rather weak compared to an order isomorphism between the involved posets, but every Galois connection gives rise to an isomorphism of certain sub-posets, as will be explained below.
• A Galois connection is rather weak compared to an order isomorphism between the involved posets, but every Galois connection gives rise to an isomorphism of certain sub-posets, as will be explained below.
• Conversely, by the order theoretical Adjoint Functor Theorem, mappings that preserve all suprema / infima can be guaranteed to be part of a unique Galois connection as long as some additional requirements are met.
• In the language of order theory, the floor function is a residuated mapping, that is, part of a Galois connection : it is the upper adjoint of the function that embeds the integers into the reals.
• In fact, more generally, one has a Galois connection between subsets of the space and subsets of the algebra, where " Zariski closure " and " radical of the ideal generated " are the closure operators.
• Conversely, any closure operator on some poset gives rise to the Galois connection with lower adjoint being just the corestriction of to the image of ( i . e . as a surjective mapping the closure system ).
• The composition of the " wrong way " map with the usual map gives a map from the homology of the base to itself, analogous to a unit / counit of an adjunction; compare also Galois connection.
• Lastly, by the lattice theorem there is a Galois connection between subgroups of O ( " n " ) and subgroups of PO ( " n " ), in particular of finite subgroups.