mathematics, a field of sets is a mathematical structure consisting of a pair ( X , F ) {\displaystyle (X,{\mathcal {F}})} consisting of a set X {\displaystyle...

Borel set is any subset of a topological space that can be formed from its open sets (or, equivalently, from closed sets) through the operations of countable...

generally, a collection of any sets whatsoever is called a family of sets, set family, or a set system. Additionally, a family of sets may be defined as a...

algebra of sets, not to be confused with the mathematical structure of an algebra of sets, defines the properties and laws of sets, the set-theoretic...

is called a ring (of sets) if it is closed under union and intersection. That is, the following two statements are true for all sets A {\displaystyle A}...

duality with topological fields of sets. The latter represent the Lindenbaum–Tarski algebra using sets of points satisfying sentences of the S4 theory in the...

mathematical field of category theory, the category of sets, denoted by Set, is the category whose objects are sets. The arrows or morphisms between sets A and...

Look up set in Wiktionary, the free dictionary. Set, The Set, SET or SETS may refer to: Set (mathematics), a collection of elements Category of sets, the...

space Field of sets, a mathematical structure of sets in an abstract space Field of a binary relation, union of its domain and its range Field of view, the...

Field of Dreams is a 1989 American sports fantasy drama film written and directed by Phil Alden Robinson, and based on Canadian novelist W. P. Kinsella's...

to a certain field of sets. The theorem is fundamental to the deeper understanding of Boolean algebra that emerged in the first half of the 20th century...

Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any...

Julia set and the Fatou set are two complementary sets (Julia "laces" and Fatou "dusts") defined from a function. Informally, the Fatou set of the function...

there are Besicovitch sets of measure zero. A Kakeya needle set (sometimes also known as a Kakeya set) is a (Besicovitch) set in the plane with a stronger...

track and a grass field for the throwing and some of the jumping events. Track and field is categorized under the umbrella sport of athletics, which also...

Field hockey (or simply hockey) is a team sport structured in standard hockey format, in which each team plays with 11 players in total, made up of 10...

A rugby league team consists of 13 players on the field, with 4 interchange players on the bench. Each of the 13 players is assigned a position, normally...

Quantum Fields on Causal Sets, PhD Thesis (Imperial College London, 2010) arXiv:1010.5514 (Quantum Field Theory) D.A. Meyer, The Dimension of Causal Sets, PhD...

both definitions involve infinite sets (Dedekind cuts and sets of the elements of a Cauchy sequence), and Cantor's set theory was published several years...

{P} (S)} , or 2S. Any subset of P(S) is called a family of sets over S. If S is the set {x, y, z}, then all the subsets of S are {} (also denoted ∅ {\displaystyle...

Knopf. The Rose Field is set directly after The Secret Commonwealth, which was published in 2019. The story follows the events of the previous book...

height and weight of an object, for each member of the data set. Data sets can also consist of a collection of documents or files. In the open data discipline...

symmetric difference of two sets, also known as the disjunctive union and set sum, is the set of elements which are in either of the sets, but not in their...

Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences...

HTTP header fields are a list of strings sent and received by both the client program and server on every HTTP request and response. These headers are...

completed with a highly optimized implementation of the general number field sieve run on hundreds of machines. No algorithm has been published that can...

set F M {\displaystyle {\mathcal {F}}_{M}} of μ ∗ {\displaystyle \mu ^{*}} -measurable sets (that is, Carathéodory-measurable sets), which is the set...

stream of charged particles emanating from the Sun. The magnetic field is generated by electric currents due to the motion of convection currents of a mixture...

In the mathematical field of topology, a Gδ set is a subset of a topological space that is a countable intersection of open sets. The notation originated...

science, a level set is a data structure designed to represent discretely sampled dynamic level sets of functions. A common use of this form of data structure...