394: Quotient Map

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A definition of quotient map

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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 continuous map.
• The reader knows a definition of surjection.

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Target Context

• The reader will have a definition of quotient map.

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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 topological spaces, $T_1,T_2$, any continuous surjection, $f:T_1\to T_2$, such that for any subset, $S\subseteq T_2$, if $f^{-1}(S)$ is open, $S$ is open

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References

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