PlanetMath: topological ring

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topological ring

(Definition)

A ring which is a topological space is called a topological ring if the addition and multiplication functions are continuous functions from $R \times R$ to .

A topological ring is defined to be a topological field if it is a field and the inversion function is continuous away from 0.

"topological ring" is owned by djao.

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Also defines:

topological field

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Cross-references: inversion, field, continuous functions, functions, multiplication, addition, topological space, ring
There are 13 references to this entry.

This is version 2 of topological ring, born on 2002-06-08, modified 2006-06-30.
Object id is 3076, canonical name is TopologicalRing.
Accessed 4747 times total.

Classification:

AMS MSC:	13J99 (Commutative rings and algebras :: Topological rings and modules :: Miscellaneous)
	12J99 (Field theory and polynomials :: Topological fields :: Miscellaneous)
	54H13 (General topology :: Connections with other structures, applications :: Topological fields, rings, etc.)

Pending Errata and Addenda

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