oriented knot造句

The knot sum of oriented knots is commutative and associative.
For oriented knots, this decomposition is also unique.
To define the connected sum for two oriented knots:
The oriented ambient isotopy classes of these four oriented knots are all distinct.
A " Wirtinger presentation " is derived from a regular projection of an oriented knot.
It's difficult to find oriented knot in a sentence. 用oriented knot造句挺难的

For the connected sum of knots to be well defined, one has to consider "'oriented knots "'in 3-space.
Under this operation, oriented knots in 3-space form a commutative monoid with unique prime factorization, which allows us to define what is meant by a prime knot.
Also, I don't really any know any general histories of knot theory ( although I know of articles on specific episodes or time periods ); besides the Silver reference for the 19th century stuff, I mainly used the stuff that appears in more historically-oriented knot theory books.
In 1949 Horst Schubert proved that every oriented knot in S ^ 3 decomposes as a connect-sum of prime knots in a unique way, up to reordering, making the monoid of oriented isotopy-classes of knots in S ^ 3 a free commutative monoid on countably-infinite many generators.