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 be a surjection; a set C in the domain of p is called saturated if for every p^-1(A) that intersects C, p^-1(A) is contained in C. This is equivalent to the statement that p⁻¹p(C)=C.

References

• G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove, and D. S. Scott (2003). "Continuous Lattices and Domains". Encyclopedia of Mathematics and its Applications. Vol. 93. Cambridge University Press. ISBN 0-521-80338-1.{{cite encyclopedia}}: CS1 maint: multiple names: authors list (link)
• J. R. Munkres (2000). Topology. Prentice-Hall. ISBN 0-13-181629-2.