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Base (topology)

In mathematics, a base (or basis; pl.: bases) for the topology τ {\displaystyle \tau } of a topological space ( X , τ ) {\displaystyle (X,\tau )} is a family B {\displaystyle {\mathcal {B}}} of open subsets of X {\displaystyle X} such that every open set of the topology is equal to the union of some sub-family of B {\displaystyle {\mathcal {B}}} . For…

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Base for the closed sets

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Base (topology)

Nodes57
Edges56
Triples2
Avg. degree1.96
Density0.035088
Components1

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Important terminology

displaystyle topology base open sets set mathcal closed tau space family basis bases topological basic collection also gamma mathbb subsets

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
continuityinstance ofMany important topological definitions0.80text
convergence can be checked using only basic open sets instead of arbitrary open setsinstance ofMany important topological definitions0.80text

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