Oplysninger om | engelsk ord NONEMPTY

Eksempler på brug af NONEMPTY i en sætning

• In mathematical analysis and in probability theory, a σ-algebra ("sigma algebra"; also σ-field, where the σ comes from the German "Summe") on a set X is a nonempty collection Σ of subsets of X closed under complement, countable unions, and countable intersections.
• Simply ask the black box to find the subset that sums to zero, then check whether it returned a nonempty set.
• From the definition of vector spaces, it follows that subspaces are nonempty, and are closed under sums and under scalar multiples.
• For example, the Euclidean topology on the plane admits as a base the set of all open rectangles with horizontal and vertical sides, and a nonempty intersection of two such basic open sets is also a basic open set.
• If an infinite set is a well-ordered set, then it must have a nonempty, nontrivial subset that has no greatest element.
• The main part of the proof will consider the case of a nonempty set, and examine the members in detail; in the case where the set is empty, the property is trivially possessed by all the members of the empty set, since there are none (see vacuous truth for more).
• A nonempty affine algebraic set V is called irreducible if it cannot be written as the union of two proper algebraic subsets.
• Since there are 31 nonempty subsets of the five known Fermat primes, there are 31 known constructible polygons with an odd number of sides.
• If a family of nonempty sets has an empty intersection, its Helly number must be at least two, so the smallest k for which the k-Helly property is nontrivial is k = 2.
• Dually, a meet-semilattice (or lower semilattice) is a partially ordered set which has a meet (or greatest lower bound) for any nonempty finite subset.
• Every set X with the cocountable topology is Lindelöf, since every nonempty open set omits only countably many points of X.
• In mathematics, the simplex category (or simplicial category or nonempty finite ordinal category) is the category of non-empty finite ordinals and order-preserving maps.
• For a line bundle L on an integral Noetherian scheme X, let s be a nonzero rational section of L (that is, a section on some nonempty open subset of L), which exists by local triviality of L.
• As nonempty perfect sets in a Polish space always have the cardinality of the continuum, and the reals form a Polish space, a set of reals with the perfect set property cannot be a counterexample to the continuum hypothesis, stated in the form that every uncountable set of reals has the cardinality of the continuum.
• Limitation of Size plus I being a set (hence the universe is nonempty) renders provable the sethood of the empty set; hence no need for an axiom of empty set.
• Another characterisation is the following: A Lyndon word has the property that it is nonempty and, whenever it is split into two nonempty substrings, the left substring is always lexicographically less than the right substring.
• Every recursively enumerable (or even hyperarithmetic) nonempty subset of this total ordering has a least element.
• By work of , a finitely generated Kleinian group is Schottky if and only if it is finitely generated, free, has nonempty domain of discontinuity, and all non-trivial elements are loxodromic.
• The empty set is vacuously a hyperconnected or irreducible space under the definition above (because it contains no nonempty open sets).
• Super Dedekind Complete (SDC) if every nonempty set, bounded above, has a countable subset with identical supremum;.

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