In mathematics, particularly in the subfields of set theory and topology, a set is said to be saturated with respect to a function if is a subset of 's domain and if whenever sends two points and to the same value then belongs to (that is, if then ). Said more succinctly, the set is called saturated if
In topology, a subset of a topological space is saturated if it is equal to an intersection of open subsets of In a T1 space every set is saturated.
X=f^{-1}(Y)} are always saturated. Arbitrary unions of saturatedsets are saturated, as are arbitrary intersections of saturatedsets. Let S {\displaystyle...
called countably saturated if it is ℵ 1 {\displaystyle \aleph _{1}} -saturated; that is, it realizes all complete types over countable sets of parameters...
set. The intersection of a family of saturatedsets is saturated. Localization of a ring Right denominator set Atiyah and Macdonald, p. 36. Lang, p. 107...
In mathematics, a measure is said to be saturated if every locally measurable set is also measurable. A set E {\displaystyle E} , not necessarily measurable...
is set ("clamped") to the maximum; if it is below the minimum, it is clamped to the minimum. The name comes from how the value becomes "saturated" once...
Look up saturated, saturation, unsaturated, or unsaturation in Wiktionary, the free dictionary. Saturation, saturated, unsaturation or unsaturated may...
system is called its partial pressure. For example, air at sea level, and saturated with water vapor at 20 °C, has partial pressures of about 2.3 kPa of water...
span of this set is a dense subset of X . {\displaystyle X.} The intersection of an arbitrary family of saturated families is a saturated family. Since...
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any...
Naive set theory is any of several theories of sets used in the discussion of the foundations of mathematics. Unlike axiomatic set theories, which are...
between sets, popularized by John Venn (1834–1923) in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships...
mathematics, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure...
mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently, a set is countable...
In set theory, a universal set is a set which contains all objects, including itself. In set theory as usually formulated, it can be proven in multiple...
mathematics, particularly set theory, a finite set is a set that has a finite number of elements. Informally, a finite set is a set which one could in principle...
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...
compact saturated subset is closed (which is the case in particular if X {\displaystyle X} is Hausdorff). Borel hierarchy Borel isomorphism Baire set Cylindrical...
mathematics, the power set (or powerset) of a set S is the set of all subsets of S, including the empty set and S itself. In axiomatic set theory (as developed...
variants of the site saturation technique, from paired site saturation (saturating two positions in every mutant in the library) to scanning site saturation...
In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable. The set of natural numbers (whose existence...
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 operations...
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