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.
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Line 20. Cf. Ezekiel 2:1.
23. Cf. Ecclesiastes 12:5.
31. V. Tristan und Isolde, i, verses 5-8.
42. Id. iii, verse 24.
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