Encyclopedia > Zariski topology

  Article Content

Zariski topology

In this topology, named after Oscar Zariski, the closed sets are the sets consisting of the mutual zeros of a finite set of polynomial equations.

This definitions indicates the kind of space that can be given a Zariski topology: for example we define the Zariski topology on a n-dimensional vector space F^n over a field F, using the definition above. That this definition yields a true topology is easily verified.

It follows easily that homomorphisms are continuous and so the Zariski topology given to some finite-dimensional vector space doesn't depend on a specific basis chosen.

From here one can generalise the definition of Zariski topology to infinite-dimensional vector spaces, projective spaces, and subsets of these.



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
Ocean Beach, New York

... units at an average density of 1,640.9/km² (4,169.6/mi²). The racial makeup of the village is 98.55% White, 0.00% African American, 0.00% Native American, ...

 
 
 
This page was created in 26.5 ms