# 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 T_{1} space every set is saturated.

An alternative definition for saturated sets comes from surjections, these definitions are not equivalent: let *p* : *X* → *Y* be a surjection; a subset *C* of *X* is called **saturated** with respect to *p* if for every *p*^{−1}(*A*) that intersects *C*, *p*^{−1}(*A*) is contained in *C*. This is equivalent to the statement that *p*^{−1}*p*(*C*)*=*C*. *

## References

- G. Gierz; K. H. Hofmann; K. Keimel; J. D. Lawson; M. Mislove & D. S. Scott (2003). "Continuous Lattices and Domains".
*Encyclopedia of Mathematics and its Applications*.**93**. Cambridge University Press. ISBN 0-521-80338-1. - J. R. Munkres (2000).
*Topology (2nd Edition)*. Prentice-Hall. ISBN 0-13-181629-2.

This article is issued from
Wikipedia.
The text is licensed under Creative
Commons - Attribution - Sharealike.
Additional terms may apply for the media files.