English Dictionary

Jordan curve theorem

noun

(topology) The theorem that states that a simple closed curve (Jordan curve) divides the plane into precisely two distinct areas.

The Jordan curve theorem is a fundamental result in topology.

意味（1）

(topology) The theorem that states that a simple closed curve (Jordan curve) divides the plane into precisely two distinct areas.

There is a vast generalization of the Jordan curve theorem to higher dimensions.

意味（2）

Used other than figuratively or idiomatically: see Jordan curve, theorem.

Some known Jordan curves in the basic topology are used to prove Jordan curve theorems that identify Jordan curves among simple closed ones in each of the four quotient pretopologies.