19: Hausdorff Topological Space

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A definition of Hausdorff topological space

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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

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Starting Context

• The reader knows a definition of topological space.
• The reader knows a definition of neighborhood of point.

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Target Context

• The reader will have a definition of Hausdorff topological 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 topological space, $T$, such that for any pair of distinct points, $p_1,p_2\in T$ such that $p_1\ne p_2$, there are any neighborhood of $p_1$, $U_{p_1}$, and any neighborhood of $p_2$, $U_{p_2}$, such that $U_{p_1}\cap U_{p_2}=\mathrm{\varnothing }$

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References

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