In mathematics, a set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be...

The subset sum problem (SSP) is a decision problem in computer science. In its most general formulation, there is a multiset S{\displaystyle S} of integers...

definitions of other related terms. The meagre subsets of a fixed space form a σ-ideal of subsets; that is, any subset of a meagre set is meagre, and the union...

Relatively compact subspace, a subset whose closure is compact Totally bounded set, a subset that can be covered by finitely many subsets of fixed size This disambiguation...

in the choice of open sets. For example, every subset can be open (the discrete topology), or no subset can be open except the space itself and the empty...

mean A is any subset of B (and not necessarily a proper subset), while others reserve A ⊂ B and B ⊃ A for cases where A is a proper subset of B. Examples:...

operation. This should not be confused with a closed manifold. By definition, a subset A{\displaystyle A} of a topological space (X,τ){\displaystyle (X,\tau )}...

a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space. The idea is that a compact space has no "punctures"...

functional analysis, a subset T{\displaystyle T} of a topological vector space X{\displaystyle X} is said to be a total subset of X{\displaystyle X} if...

(or relatively compact subset, or precompact subset) Y of a topological space X is a subset whose closure is compact. Every subset of a compact topological...

V=∅.{\displaystyle V=\varnothing .} By the definition of subset, the empty set is a subset of any set A. That is, every element x of ∅{\displaystyle...

abstract algebra, a multiplicatively closed set (or multiplicative set) is a subset S of a ring R such that the following two conditions hold: 1∈S{\displaystyle...

In topology and related areas of mathematics, a subset A of a topological space X is said to be dense in X if every point of X either belongs to A or else...

define a product of group subsets in a natural way. If S and T are subsets of a group G, then their product is the subset of G defined by ST={st:s∈S and t∈T}...

geometry, a subset of a Euclidean space, or more generally an affine space over the reals, is convex if, given any two points in the subset, the subset contains...

In mathematical optimization, the ordered subset expectation maximization (OSEM) method is an iterative method that is used in computed tomography. In...

Light is a real-time strategy roguelite game created by indie developer Subset Games, which was released for Microsoft Windows, macOS and Linux in September...

schema of specification, also known as the axiom schema of separation, subset axiom scheme or axiom schema of restricted comprehension is an axiom schema...

The multiple subset sum problem is an optimization problem in computer science and operations research. It is a generalization of the subset sum problem...

In mathematics, a cocountable subset of a set X is a subset Y whose complement in X is a countable set. In other words, Y contains all but countably many...

In topology, a branch of mathematics, a subset E{\displaystyle E} of a topological space X{\displaystyle X} is said to be locally closed if any of the...

theory of computation and automata theory, the powerset construction or subset construction is a standard method for converting a nondeterministic finite...

set with n elements is sometimes called an n-set and a subset with k elements is called a k-subset. For example, the set {5,6,7}{\displaystyle \{5,6,7\}}...

Feature selection is the process of selecting a subset of relevant features (variables, predictors) for use in model construction. Stylometry and DNA microarray...

that A{\displaystyle A} is a clopen subset of Q.{\displaystyle \mathbb {Q} .} (A{\displaystyle A} is not a clopen subset of the real line R{\displaystyle...

bounded set is not necessarily a closed set and vice versa. For example, a subset S of a 2-dimensional real space R2 constrained by two parabolic curves x2...

(nonempty) irreducible closed subset of X is the closure of exactly one point of X: that is, every irreducible closed subset has a unique generic point....

In mathematics, a cofinite subset of a set X{\displaystyle X} is a subset A{\displaystyle A} whose complement in X{\displaystyle X} is a finite set. In...

described generatively as follows. For a collection T of subsets of X (that is, for any subset of the power set P(X) of X), let Tσ{\displaystyle T_{\sigma...

In mathematics, a subset B⊆A{\displaystyle B\subseteq A} of a preordered set (A,≤){\displaystyle (A,\leq )} is said to be cofinal or frequent in A{\displaystyle...