Saturated set

In mathematics, in particular in topology, a subset of a topological space (X, τ) is saturated if it is an intersection of open subsets of X. In a T₁ space every set is saturated.

Saturated sets can also be defined in terms of surjections: let p : X → Y be a surjection; a subset C of X is called saturated with respect to p if for every p(A) that intersects C, p(A) is contained in C. This is equivalent to the statement that pp(C)=C.

单词	Saturated set
释义	Saturated set 英语百科 Saturated set In mathematics, in particular in topology, a subset of a topological space (X, τ) is saturated if it is an intersection of open subsets of X. In a T₁ space every set is saturated. Saturated sets can also be defined in terms of surjections: let p : X → Y be a surjection; a subset C of X is called saturated with respect to p if for every p(A) that intersects C, p(A) is contained in C. This is equivalent to the statement that pp(C)=C.
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