154: Net with Directed Indices Set

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A definition of net with directed indices set

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Topics

About: topological 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 directed set.
• The reader knows a definition of topological space.
• The reader knows a definition of map.

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Target Context

• The reader will have a definition of net with directed indices set.

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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

For any directed set, $S$, and any topological space, $T$, any map, $f:S\to T$

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2: Note

Any sequence on any topological space is a net with directed indices set, because the natural numbers set (whether it includes $0$ or not) is a directed indices set and the sequence is a map from the natural numbers set into the topological space.

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References

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