8: Topology

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A definition of topology

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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 set.

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Target Context

• The reader will have a definition of topology.

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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 set, S, a set of some subsets (called open sets), O, such that 1) $\mathrm{\varnothing }\in O$ and $S\in O$ 2) for any $U_1\in O$ and any $U_2\in O$, $U_1\cap V_2\in O$ 3) for any $U_{\alpha }\in O$ where $\alpha \in A$ where A is any index set not necessarily countable, $({\cup }_{\alpha }{U}_{\alpha })\in O$

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References

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