A map between topological spaces that maps closed sets to closed sets. If is bijective, then
where denotes the inverse map. In particular, a homeomorphism can be characterized as a continuous bijection which is open (or, equivalently, closed).
A map between topological spaces that maps closed sets to closed sets. If is bijective, then
where denotes the inverse map. In particular, a homeomorphism can be characterized as a continuous bijection which is open (or, equivalently, closed).
This entry contributed by Margherita Barile
Barile, Margherita. "Closed Map." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ClosedMap.html