Informatie over | Engels woord NON-EMPTY

Voorbeelden van het gebruik van NON-EMPTY in een zin

• In mathematics, the axiom of choice, abbreviated AC or AoC, is an axiom of set theory equivalent to the statement that a Cartesian product of a collection of non-empty sets is non-empty.
• In mathematics, the axiom of regularity (also known as the axiom of foundation) is an axiom of Zermelo–Fraenkel set theory that states that every non-empty set A contains an element that is disjoint from A.
• In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint non-empty open subsets.
• Moreover, the Banach fixed-point theorem states that every contraction mapping on a non-empty complete metric space has a unique fixed point, and that for any x in M the iterated function sequence x, f (x), f (f (x)), f (f (f (x))),.
• This definition of cofinality relies on the axiom of choice, as it uses the fact that every non-empty set of cardinal numbers has a least member.
• For all domains in lower levels, it is the last part of the domain name, that is, the last non-empty label of a fully qualified domain name.
• A set X is well-ordered by a strict total order if every non-empty subset of X has a least element under the ordering.
• Dedekind cuts can be generalized from the rational numbers to any totally ordered set by defining a Dedekind cut as a partition of a totally ordered set into two non-empty parts A and B, such that A is closed downwards (meaning that for all a in A, x ≤ a implies that x is in A as well) and B is closed upwards, and A contains no greatest element.
• As elsewhere in graph theory, the order-zero graph (graph with no vertices) is generally not considered to be a tree: while it is vacuously connected as a graph (any two vertices can be connected by a path), it is not 0-connected (or even (−1)-connected) in algebraic topology, unlike non-empty trees, and violates the "one more vertex than edges" relation.
• Moreover, all three can be defined as the number of partitions of n elements into k non-empty subsets, where each subset is endowed with a certain kind of order (no order, cyclical, or linear).
• Likewise, it is analogous to the finite intersection property characterization of compactness in topological spaces: a collection of closed sets in a compact space has a non-empty intersection if every finite subcollection has a non-empty intersection.
• In mathematics, the well-ordering principle states that every non-empty subset of nonnegative integers contains a least element.
• For example, a "function from the reals to the reals" may refer to a real-valued function of a real variable whose domain is a proper subset of the real numbers, typically a subset that contains a non-empty open interval.
• It is vacuously true that all of the subsets in this family are non-empty subsets of the empty set and that they are pairwise disjoint subsets of the empty set, because there are no subsets to have these unlikely properties.
• Also, the non-normal numbers (as well as the normal numbers) are dense in the reals: the set of non-normal numbers between two distinct real numbers is non-empty since it contains every rational number (in fact, it is uncountably infinite and even comeagre).
• Corollary: It follows that the Smith set is the smallest non-empty dominating set, and that it is well defined.
• Thus, to prove this equality, it suffices to prove that it is verified on a non-empty open subset (for the usual topology, or, more generally, for the Zariski topology) of the space of all the coefficients.
• the order on R is complete, in the sense that every non-empty bounded subset has a supremum and an infimum; and.
• In a formulation due to Karl Weierstrass, this theorem states that a continuous function from a non-empty compact space to a subset of the real numbers attains a maximum and a minimum.
• It makes sense to consider all the long spaces at once because every connected (non-empty) one-dimensional (not necessarily separable) topological manifold possibly with boundary, is homeomorphic to either the circle, the closed interval, the open interval (real line), the half-open interval, the closed long ray, the open long ray, or the long line.

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