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Alexandroff extension

In the mathematical field of topology, the Alexandroff extension is a way to extend a noncompact topological space by adjoining a single point in such a way that the resulting space is compact. It is named after the Russian mathematician Pavel Alexandroff. More precisely, let X be a topological space. Then the Alexandroff extension of X is a certain…

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HomeomorphicDiscrete topologyPolyadic spacesWedge of n {\displaystyle n} circlesHawaiian earring
10 related topics

Overview

MathematicalTopologyTopological spaceCompactPavel Alexandroff
12 related topics

The Alexandroff extension

Kelley 1975T1
2 related topics

The one-point compactification

Limit pointIsolated point
2 related topics

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The Alexandroff extension

The one-point compactification

Non-Hausdorff one-point compactifications

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Alexandroff extension

Nodes34
Edges33
Triples36
Avg. degree1.94
Density0.058824
Components1

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Alexandroff extension

Top relations

related to Compactifications of continuous spaces · 15
Alexandroff extension → Alexandroff, As, Euclidean, Given, Hausdorff, Hawaiian, However, If, Recall, Rn, Since, Sn, The, This, X/C
related to The Alexandroff extension · 9
Alexandroff extension → Alexandroff, Here, Kelley, Let, Note, Put, Sometimes, The, Willard
related to As a functor · 7
Alexandroff extension → Alexandroff, Arr, Func, In, The, The Alexandroff, Top
related to The one-point compactification · 4
Alexandroff extension → Alexandroff, Hausdorff, In, Recall
is a · 1
Alexandroff extension → way to extend a noncompact topological space by adjoining a single point in such a way that the resulting space is compact

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Important terminology

displaystyle space compact compactification alexandroff hausdorff one-point topology extension topological infty noncompact open point locally spaces closed embedding stereographic projection

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SubjectPredicateObjectConfidenceSrc
Alexandroff extensionis away to extend a noncompact topological space by adjoining a single point in such a way that the resulting space is compact0.90text
Alexandroff extensionrelated to As a functorThe Alexandroff0.60section
Alexandroff extensionrelated to As a functorIn0.60section
Alexandroff extensionrelated to As a functorAlexandroff0.60section
Alexandroff extensionrelated to As a functorThe0.60section
Alexandroff extensionrelated to As a functorArr0.60section
Alexandroff extensionrelated to As a functorFunc0.60section
Alexandroff extensionrelated to As a functorTop0.60section
Alexandroff extensionrelated to Compactifications of continuous spacesThe0.60section
Alexandroff extensionrelated to Compactifications of continuous spacesEuclidean0.60section
Alexandroff extensionrelated to Compactifications of continuous spacesRn0.60section
Alexandroff extensionrelated to Compactifications of continuous spacesSn0.60section

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