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| {{Noref|date=November 2009}}
| | The author is known as Irwin Wunder but it's not the most masucline name out there. To gather coins is what his family members and him enjoy. Years ago we moved to North Dakota. She is a librarian but she's usually needed her own company.<br><br>my blog :: home std test ([http://blogzaa.com/blogs/post/9199 Keep Reading]) |
| In [[mathematics]], a '''topological algebra''' ''A'' over a [[topological field]] '''K''' is a [[topological vector space]] together with a continuous multiplication
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| :<math>\cdot :A\times A \longrightarrow A</math>
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| :<math>(a,b)\longmapsto a\cdot b</math>
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| that makes it an [[algebra over a field|algebra]] over '''K'''. A unital [[associative algebra|associative]] topological algebra is a [[topological ring]].
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| An example of a topological algebra is the algebra C[0,1] of continuous real-valued functions on the closed unit interval [0,1],
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| or more generally any [[Banach algebra]].
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| The term was coined by [[David van Dantzig]]; it appears in the title of his [[Thesis|doctoral dissertation]] (1931).
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| 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 {id<sub>[0,1]</sub>} consisting only of the identity function id<sub>[0,1]</sub> is a generating set of the Banach algebra C[0,1].
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| [[Category:Topological vector spaces]]
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| [[Category:Topological algebra]]
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| [[Category:Algebras]] | |
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| {{topology-stub}}
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Latest revision as of 17:55, 25 August 2014
The author is known as Irwin Wunder but it's not the most masucline name out there. To gather coins is what his family members and him enjoy. Years ago we moved to North Dakota. She is a librarian but she's usually needed her own company.
my blog :: home std test (Keep Reading)