377: Accumulation Value of Net with Directed Index Set

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A definition of accumulation value of net with directed index 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 net with directed index set.

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Target Context

• The reader will have a definition of accumulation value of net with directed index 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, $S$, any topological space, $T$, and any net with directed index set, $f:S\to T$, any point, $p\in T$, such that for any neighborhood, $N_p\subseteq T$, of $p$ and any index $i_0\in S$, there is an index, $i\in S$, such that $i_0\le i$ and $f(i)\in N_p$

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2: Note

A net with directed index set can have multiple accumulation values.

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References

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