set of rational numbers
11Vitali set — In mathematics, a Vitali set is an elementary example of a set of real numbers that is not Lebesgue measurable. The Vitali theorem is the existence theorem that there are such sets. It is a non constructive result. The naming is for Giuseppe… …
12Complement (set theory) — In set theory, a complement of a set A refers to things not in (that is, things outside of), A. The relative complement of A with respect to a set B, is the set of elements in B but not in A. When all sets under consideration are considered to be …
13Fσ set — In mathematics, an Fσ set (said F sigma set) is a countable union of closed sets. The notation originated in France with F for ( French : closed) and σ for ( French : sum, union).In metrizable spaces, every open set is an Fσ set. The complement… …
14Nowhere dense set — A subset A of a topological space X is nowhere dense in X if and only if the interior of the closure of A is empty. The order of operations is important. For example, the set of rational numbers, as a subset of R has the property that the closure …
15Rational variety — In mathematics, a rational variety is an algebraic variety, over a given field K, which is birationally equivalent to projective space of some dimension over K. This is a question on its function field: is it up to isomorphism the field of all… …
16Construction of the real numbers — In mathematics, there are several ways of defining the real number system as an ordered field. The synthetic approach gives a list of axioms for the real numbers as a complete ordered field. Under the usual axioms of set theory, one can show that …
17Countable set — Countable redirects here. For the linguistic concept, see Count noun. Not to be confused with (recursively) enumerable sets. In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of… …
18Naive set theory — This article is about the mathematical topic. For the book of the same name, see Naive Set Theory (book). Naive set theory is one of several theories of sets used in the discussion of the foundations of mathematics.[1] The informal content of… …
19Closed set — This article is about the complement of an open set. For a set closed under an operation, see closure (mathematics). For other uses, see Closed (disambiguation). In geometry, topology, and related branches of mathematics, a closed set is a set… …
20Gδ set — 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 in Germany with G for ( German : area) meaning open set in this case and δ for ( German :… …
