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:
“Though there were numerous vessels at this great distance in the horizon on every side, yet the vast spaces between them, like the spaces between the stars,far as they were distant from us, so were they from one another,nay, some were twice as far from each other as from us,impressed us with a sense of the immensity of the ocean, the unfruitful ocean, as it has been called, and we could see what proportion man and his works bear to the globe.”
—Henry David Thoreau (18171862)