preimage of set
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preimage — noun The set containing exactly every member of the domain of a function such that the member is mapped by the function onto an element of a given subset of the codomain of the function. Formally, of a subset B of the codomain Y under a function… … Wiktionary
Implementation of mathematics in set theory — This article examines the implementation of mathematical concepts in set theory. The implementation of a number of basic mathematical concepts is carried out in parallel in ZFC (the dominant set theory) and in NFU, the version of Quine s New… … Wikipedia
Null set — In mathematics, a null set is a set that is negligible in some sense. For different applications, the meaning of negligible varies. In measure theory, any set of measure 0 is called a null set (or simply a measure zero set). More generally,… … Wikipedia
Descriptive set theory — In mathematical logic, descriptive set theory is the study of certain classes of well behaved subsets of the real line and other Polish spaces. As well as being one of the primary areas of research in set theory, it has applications to other… … Wikipedia
Universally Baire set — In the mathematical field of descriptive set theory, a set of reals (or subset of the Baire space or Cantor space) is called universally Baire if it has a certain strong regularity property. Universally Baire sets play an important role in Ω… … Wikipedia
Power set — In mathematics, given a set S , the power set (or powerset) of S , written mathcal{P}(S), P ( S ), or 2 S , is the set of all subsets of S . In axiomatic set theory (as developed e.g. in the ZFC axioms), the existence of the power set of any set… … Wikipedia
Open set — Example: The points (x, y) satisfying x2 + y2 = r2 are colored blue. The points (x, y) satisfying x2 + y2 < r2 are colored red. The red points form an open set. The blue points form a closed set. The union of the red and blue points is a… … Wikipedia
Recursively enumerable set — In computability theory, traditionally called recursion theory, a set S of natural numbers is called recursively enumerable, computably enumerable, semidecidable, provable or Turing recognizable if: There is an algorithm such that the set of… … Wikipedia
Recursive set — In computability theory, a set of natural numbers is called recursive, computable or decidable if there is an algorithm which terminates after a finite amount of time and correctly decides whether or not a given number belongs to the set. A more… … Wikipedia
Cylinder set — In mathematics, a cylinder set is the natural open set of a product topology. Cylinder sets are particularly useful in providing the base of the natural topology of the product of a countable number of copies of a set. If V is a finite set, then… … Wikipedia
Inductive set — This article relates to the notion of inductive sets from descriptive set theory. For the notion in the context of the axiom of infinity, see Inductive set (axiom of infinity). In descriptive set theory, an inductive set of real numbers (or more… … Wikipedia
