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...

(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...

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...

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...

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...

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

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...

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...

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:...

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"...

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...

∅ . {\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...

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...

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}...

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...

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

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 S T = { s t...

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

FTL: Faster Than Light is a roguelike game created by indie developer Subset Games, which was released for Windows, MacOS, and Linux in September 2012...

specification, also known as the axiom schema of separation (Aussonderungsaxiom), subset axiom, axiom of class construction, or axiom schema of restricted comprehension...

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...

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 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...

An agreeable subset is a subset of items that is considered, by all people in a certain group, to be at least as good as its complement. Finding a small...

In machine learning, feature selection is the process of selecting a subset of relevant features (variables, predictors) for use in model construction...

every finite subset of A {\displaystyle A} has an upper bound. In this definition, the existence of an upper bound of the empty subset implies that A...

mathematics, a subset of a given set is closed under an operation of the larger set if performing that operation on members of the subset always produces...

convex curve. The intersection of all the convex sets that contain a given subset A of Euclidean space is called the convex hull of A. It is the smallest...

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 T σ {\displaystyle T_{\sigma...