The basis criterion (topology)/Statement
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Statement
Let (X,J) be a topological space and let B∈P(P(X)) be a topological basis for (X,J). Then[1]:
- ∀U∈P(X)[U∈J⟺∀p∈U∃B∈B[p∈B⊆U]⏟basis criterion][Note 1]
If a subset U of X satisfies[Note 2] ∀p∈U∃B∈B[p∈B⊆U] we say it satisfies the basis criterion with respect to B[1]
Notes
- Jump up ↑ Note that when we write p∈B⊆U we actually mean p∈B∧B⊆U. This is a very slight abuse of notation and the meaning of what is written should be obvious to all without this note
- Jump up ↑ This means "if a U∈P(X) satisfies...
References
