Zariski's Main Theorem: Topological Form
A topological version of Zariski's main theorem says that if x is a (closed) point of a normal complex variety then there are arbitrarily small neighborhoods U of x such that the set of non-singular points of U is connected (Mumford 1999, III.9).
Read more about this topic: Zariski's Main Theorem
Famous quotes containing the words main and/or form:
“The chief misery of the decline of the faculties, and a main cause of the irritability that often goes with it, is evidently the isolation, the lack of customary appreciation and influence, which only the rarest tact and thoughtfulness on the part of others can alleviate.”
—Charles Horton Cooley (1864–1929)
“Now, what I want is, Facts. Teach these boys and girls nothing but Facts. Facts alone are wanted in life. Plant nothing else, and root out everything else. You can only form the minds of reasoning animals upon Facts: nothing else will ever be of any service to them. This is the principle on which I bring up my own children, and this is the principle on which I bring up these children. Stick to Facts, sir!”
—Charles Dickens (1812–1870)