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Meagre set

In the mathematical field of general topology, a meagre set (also called a meager set or a set of first category) is a subset of a topological space that is a countable union of subsets whose closures have empty interior. Thus meager sets are, in a sense, "small", being small unions of small subsets.

Characters, Examples & Characterizations and sufficient conditions

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Overview

Definitions

Examples

Characterizations and sufficient conditions

Properties

Banach–Mazur game

Erdos–Sierpinski duality

Bibliography

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Meagre set

Nodes63
Edges62
Triples33
Avg. degree1.97
Density0.031746
Components1

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Meagre set

Top relations

related to Banach–Mazur game · 10
Meagre set → Banach, For, In, Let, Mazur, Meagre, MZ, Player, Then, Theorem
related to Meagre subsets and Lebesgue measure · 7
Meagre set → Cantor, For, Lebesgue, Smith, The, There, Volterra
related to Characterizations and sufficient conditions · 6
Meagre set → Baire, By, Consequently, Every, Hausdorff, However
related to Erdos–Sierpinski duality · 5
Meagre set → In, Lebesgue, Many, Sierpinski, The Erdos
related to Definitions · 3
Meagre set → See, The, Throughout
related to Relation to Borel hierarchy · 2
Meagre set → Dually, Just

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Important terminology

displaystyle meagre space nonmeagre set subset sets dense nowhere every topological category subsets countable open mathbb comeagre measure interior subspace

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Meagre setrelated to Banach–Mazur gameMeagre0.60section
Meagre setrelated to Banach–Mazur gameBanach0.60section
Meagre setrelated to Banach–Mazur gameMazur0.60section
Meagre setrelated to Banach–Mazur gameLet0.60section
Meagre setrelated to Banach–Mazur gameThen0.60section
Meagre setrelated to Banach–Mazur gameMZ0.60section
Meagre setrelated to Banach–Mazur gameIn0.60section
Meagre setrelated to Banach–Mazur gamePlayer0.60section
Meagre setrelated to Banach–Mazur gameTheorem0.60section
Meagre setrelated to Banach–Mazur gameFor0.60section
Meagre setrelated to Characterizations and sufficient conditionsEvery0.60section
Meagre setrelated to Characterizations and sufficient conditionsBaire0.60section

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