complete lattice वाक्य
उदाहरण वाक्य
मोबाइल
- The Scott topology was first defined by Dana Scott for complete lattices and later defined for arbitrary partially ordered sets.
- This order has the desirable property that every subset has a supremum and an infimum : it is a complete lattice.
- Every complete lattice is also a bounded lattice, which is to say that it has a greatest and least element.
- A complete lattice is "'completely distributive "'if for all such data the following statement holds:
- Completely distributive complete lattices ( also called " completely distributive lattices " for short ) are indeed highly special structures.
- When considering directed complete partial orders or complete lattices the additional requirements that the specified suprema exist can of course be dropped.
- A lattice in which every subset, not just every pair, possesses a meet and a join is a complete lattice.
- Since the definition also assures the existence of binary meets and joins, complete lattices thus form a special class of bounded lattices.
- The aforementioned result that free complete lattices do not exist entails that an according free construction from a poset is not possible either.
- In summary, one can say that every complete lattice is isomorphic to the image of a closure operator on a powerset lattice.
- Without the finiteness restriction a posetal category with all products is automatically cocomplete, and dually, by a theorem about complete lattices.
- *PM : complete lattice homomorphism, id = 9241 new !-- WP guess : complete lattice homomorphism-- Status:
- *PM : complete lattice homomorphism, id = 9241 new !-- WP guess : complete lattice homomorphism-- Status:
- More generally, these definitions make sense in any partially ordered set, provided the infima exist, such as in a complete lattice.
- More special versions of both are continuous and algebraic continuous lattices and algebraic lattices, which are just complete lattices with the respective properties.
- Complete distributivity is a self-dual property, i . e . dualizing the above statement yields the same class of complete lattices.
- Would there be a free construction of complete lattices from posets, then both constructions could be composed, which contradicts the negative result above.
- Let ( L, \ leq ) be a complete lattice, with infimum and supremum symbolized by \ wedge and \ vee, respectively.
- Complete distributivity is again a self-dual property, i . e . dualizing the above statement yields the same class of complete lattices.
- If is a partially ordered set, a " completion " of means a complete lattice with an order-embedding of into.
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