A proper map is a continuous map 
for which the inverse
image of every compact set in 
is compact in 
. For locally compact Hausdorff
spaces, this is equivalent to requiring that 
be a closed map with compact
fibers.
Proper Map
See also
Closed Map, Compact Set, Continuous Function, Inverse ImageExplore with Wolfram|Alpha
References
Bourbaki, N. General Topology: Chapters 1-4. Berlin, Germany: Springer-Verlag, 1998.Cite this as:
Weisstein, Eric W. "Proper Map." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ProperMap.html