In Topological Spaces
If X and Y are topological spaces and f is a continuous function between them, then the topological properties of ker f can shed light on the spaces X and Y. For example, if Y is a Hausdorff space, then ker f must be a closed set. Conversely, if X is a Hausdorff space and ker f is a closed set, then the coimage of f, if given the quotient space topology, must also be a Hausdorff space.
Read more about this topic: Kernel (set Theory)
Famous quotes containing the word spaces:
“Le silence éternel de ces espaces infinis m’effraie. The eternal silence of these infinite spaces frightens me.”
—Blaise Pascal (1623–1662)