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Pointclass

In the mathematical field of descriptive set theory, a pointclass is a collection of sets of points, where a point is ordinarily understood to be an element of some perfect Polish space. In practice, a pointclass is usually characterized by some sort of definability property; for example, the collection of all open sets in some fixed collection of Polish…

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Overview

Basic framework

Boldface pointclasses

Lightface pointclasses

Advanced semantic analysis

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Map overview Semantic statistics

Pointclass

Nodes47
Edges46
Triples31
Avg. degree1.96
Density0.042553
Components1

How this topic connects Entity context

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Pointclass

Top relations

related to Boldface pointclasses · 14
Pointclass → Boldface, Borel, Delta, For, Fσ, Greek, Gδ, In, Pi, Polish, Sets, Sigma, The, Therefore
related to Basic framework · 9
Pointclass → Baire, Cantor, Cartesian, In, Polish, Sigma, Then, This, Yiannis Moschovakis
is a · 3
Pointclass → collection of sets of points, definability property, downward-closed union of Wadge degrees

Important terminology Word statistics

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Important terminology

sets set displaystyle collection open pointclasses sigma space polish lightface boldface computable boldsymbol pi example spaces theory property may perfect

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Pointclassis acollection of sets of points0.90text
Pointclassis adefinability property0.90text
Pointclassis adownward-closed union of Wadge degrees0.90text
Lebesgue measurabilityinstance ofhave regularity properties0.80text
Baire space or sometimes Cantor spaceinstance ofdescriptive set theorists often simplify matters by working in a fixed Polish space0.80text
each of which has the advantage of being zero dimensionalinstance ofdescriptive set theorists often simplify matters by working in a fixed Polish space0.80text
and indeed homeomorphic to its finite or countable powersinstance ofdescriptive set theorists often simplify matters by working in a fixed Polish space0.80text
so that considerations of dimensionality never ariseinstance ofdescriptive set theorists often simplify matters by working in a fixed Polish space0.80text
Pointclassrelated to Basic frameworkIn0.60section
Pointclassrelated to Basic frameworkPolish0.60section
Pointclassrelated to Basic frameworkBaire0.60section
Pointclassrelated to Basic frameworkCantor0.60section

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    Min side: 3
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