specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship between...
25 KB (3,467 words) - 11:27, 10 January 2024
isomorphic, with a unique isomorphism. The isomorphism theorems provide canonical isomorphisms that are not unique. The term isomorphism is mainly used for algebraic...
15 KB (2,196 words) - 09:56, 18 August 2024
Thom space (redirect from Thom isomorphism theorem)
B} be a real vector bundle of rank n. Then there is an isomorphism called a Thom isomorphism Φ : H k ( B ; Z 2 ) → H ~ k + n ( T ( E ) ; Z 2 ) , {\displaystyle...
13 KB (1,978 words) - 18:32, 31 July 2024
order theory and model theory, branches of mathematics, Cantor's isomorphism theorem states that every two countable dense unbounded linear orders are...
25 KB (3,028 words) - 20:53, 28 July 2024
in accordance with the general notion of isomorphism being a structure-preserving bijection. If an isomorphism exists between two graphs, then the graphs...
13 KB (1,637 words) - 18:31, 10 August 2024
two are isometrically anti-isomorphic. The (anti-) isomorphism is a particular natural isomorphism. Let H {\displaystyle H} be a Hilbert space over a...
75 KB (12,630 words) - 11:15, 13 July 2024
Topological group (redirect from Birkhoff–Kakutani theorem)
and only if it is continuous at some point. An isomorphism of topological groups is a group isomorphism that is also a homeomorphism of the underlying...
50 KB (7,492 words) - 16:51, 25 May 2024
kernel and image of the homomorphism. The homomorphism theorem is used to prove the isomorphism theorems. Given two groups G and H and a group homomorphism...
8 KB (1,307 words) - 20:37, 15 March 2024
T)=\dim(\operatorname {Domain} (T)).} This theorem can be refined via the splitting lemma to be a statement about an isomorphism of spaces, not just dimensions....
18 KB (3,066 words) - 16:26, 18 April 2024
of a ring Isomorphism theorems theorems that assert that some homomorphisms involving quotients and subobjects are isomorphisms Isomorphism (sociology)...
1 KB (200 words) - 19:22, 13 July 2022