English Dictionary

Zariski topology

名詞

(algebraic geometry) Originally, a topology applicable to algebraic varieties, such that the closed sets are the variety's algebraic subvarieties; later, a generalisation in which the topological space is the set of prime ideals of a commutative ring and is called the spectrum of the ring.

日本語の意味

ザリスキー位相：元々は代数幾何学において代数多様体に適用される位相で、閉集合がその多様体の代数的部分多様体となるもの。 / ザリスキー位相：後に一般化され、可換環の素イデアル全体を位相空間（スペクトル）として捉えるもの。

When exploring intersections of algebraic sets, the counterintuitive notion of closeness in the Zariski topology often surprises students.

代数集合の交点を調べると、閉集合が代数部分多様体であるような多様体上の位相（ザリスキ位相）における直感に反する「近さ」の概念は学生を驚かせることが多い。

意味（1）

(algebraic geometry) Originally, a topology applicable to algebraic varieties, such that the closed sets are the variety's algebraic subvarieties; later, a generalisation in which the topological space is the set of prime ideals of a commutative ring and is called the spectrum of the ring.

The Zariski topology allows tools from topology to be used in the study of algebraic varieties, even when the underlying field is not a topological field.

Zariski topologies （ plural ）