Second Isomorphism Theorem

The following theorem is called the Second Isomorphism Theorem for schemes. 

Note that the Homomorphism Theorem and the First Isomorphism Theorem deal with factorizations over arbitrary closed subsets, whereas the Second Isomorphism Theorem deals with factorizations over normal closed subsets. 

We shall generalize the Second Isomorphism Theorem in the next section. 

Pontjagin s theorem is as follows [22]. Let T be a locally compact, connected topological field satisfying the second axiom of countability. Then T is isomorphic with one of the three topological fields (1) the held of real numbers, (2) the held of complex numbers, and (3) the held of quaternions. 

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