444: Banach Space

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A definition of Banach space

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Topics

About: vectors space

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The table of contents of this article

• Starting Context
• Target Context
• Orientation
• Main Body
• 1: Definition
• 2: Note

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Starting Context

• The reader knows a definition of normed vectors space.
• The reader knows a definition of metric induced by norm.
• The reader knows a definition of complete metric space.

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Target Context

• The reader will have a definition of Banach space.

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Orientation

There is a list of definitions discussed so far in this site.

There is a list of propositions discussed so far in this site.

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Main Body

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1: Definition

Any normed vectors space that is a complete metric space with the metric induced by the norm

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2: Note

Being complete is about metric space, so, the vectors space has to be given the metric.

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References

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