of descriptive set theory, a subset of a Polish space has the perfect set property if it is either countable or has a nonempty perfect subset (Kechris 1995...

confusion, also note that having the perfect set property is not the same as being a perfect set. Examples of perfect subsets of the real line R {\displaystyle...

real line are well behaved (in particular, measurable and with the perfect set property). AD can be used to prove that the Wadge degrees have an elegant...

of a Polish space have the property of Baire and the perfect set property. Modern descriptive set theory includes the study of the ways in which these...

indeed universal measurability), the property of Baire, and the perfect set property. In practice, descriptive set theorists often simplify matters by...

extension V[G] such that every set of reals is Lebesgue measurable, has the perfect set property, and has the Baire property. Solovay constructed his model...

applied in descriptive set theory to show that Borel sets in Polish spaces have regularity properties such as the perfect set property. The theorem is also...

Analytic sets are always Lebesgue measurable (indeed, universally measurable) and have the property of Baire and the perfect set property. When A {\displaystyle...

In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of unintuitive properties. It was discovered in 1874...

non-measurable set of real numbers, or that there is a set of real numbers without the property of Baire or without the perfect set property. This follows...

Descriptive set theory Analytic set Analytical hierarchy Borel equivalence relation Infinity-Borel set Lightface analytic game Perfect set property Polish...

a non-empty family A of subsets of a set X {\displaystyle X} is said to have the finite intersection property (FIP) if the intersection over any finite...

Set of uniqueness Property of Baire Lebesgue measurable Universally measurable set Perfect set property Universally Baire set Meager set Comeager set...

set of reals has the property of Baire, is Lebesgue measurable (in fact universally measurable) and has the perfect set property. The first periodicity...

Descriptive set theory Analytic set Analytical hierarchy Borel equivalence relation Infinity-Borel set Lightface analytic game Perfect set property Polish...

or AD, implies that every set of reals is Lebesgue measurable, has the property of Baire, and has the perfect set property (all three of these results...

families. For instance, in all perfect graphs, the graph coloring problem, maximum clique problem, and maximum independent set problem can all be solved in...

and Spencer as they try to find the perfect home for a different set of buyers each week. A cliché used by property experts is that the three most important...

that all projective sets are Lebesgue measurable (in fact, universally measurable) and have the perfect set property and the property of Baire. It also...

and Jonathan for the book Dream Home: The Property Brothers' Ultimate Guide to Finding & Fixing Your Perfect House. It was released April 4, 2016 and debuted...

In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number...

a countable union of nowhere dense sets), and the perfect set property (is either countable or contains a perfect subset). The consistency of the existence...

measurable (in fact, universally measurable) and has the property of Baire and the perfect set property. L(R) does not satisfy the axiom of uniformization or...

numbers in sports)—which do not have the properties of numbers in a mathematical sense. The natural numbers form a set, commonly symbolized as a bold N or...

in G is a subset M of edge set E, such that every vertex in the vertex set V is adjacent to exactly one edge in M. A perfect matching is also called a...

Perfect Strangers is an American sitcom that ran for eight seasons, from March 25, 1986, to August 6, 1993, on the ABC television network. Created by...

equilibrium theory, a perfect market, also known as an atomistic market, is defined by several idealizing conditions, collectively called perfect competition,...

are the perfect designing duo". Toronto Star. Archived from the original on March 6, 2013. Retrieved January 17, 2012. "Interview: Property Brothers...

graphs by their forbidden induced subgraphs. A perfect graph is an undirected graph with the property that, in every one of its induced subgraphs, the...

desired property. For instance, a chordal completion is a supergraph that is a chordal graph. 3.  A complete matching is a synonym for a perfect matching;...