Topological algebra

Topological Algebra

Topological algebra

to get instant updates about 'Topological Algebra' on your MyPage. Meet other similar minded people. Its Free!


All Updates

In mathematics, a topological algebra A over a topological field K is a topological vector space together with a continuous multiplication

<math>cdot :Atimes A longrightarrow A</math>
<math>(a,b)longmapsto acdot b</math>

that makes it an algebra over K. A unital associative topological algebra is a topological ring.An example of a topological algebra is the algebra C of continuous real-valued functions on the closed unit interval ,or more generally any Banach algebra.

The term was coined by David van Dantzig; it appears in the title of his doctoral dissertation (1931).

The natural notion of subspace in a topological algebra is that of a (topologically) closed subalgebra. A topological algebra A is said to be generated by a subset S if A itself is the smallest closed subalgebra of A that contains S. For example by the Stone–Weierstrass theorem, the set consisting only of the identity function id<sub></sub> is a generating set of the Banach algebra C.

Read More

No feeds found

wait Posting your question. Please wait!...

No updates available.
No messages found
Tell your friends >
about this page
 Create a new Page
for companies, colleges, celebrities or anything you like.Get updates on MyPage.
Create a new Page
 Find your friends
  Find friends on MyPage from