41: Map Continuous at Point

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A definition of map continuous at point

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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 map.

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Target Context

• The reader will have a definition of map continuous at point.

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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, $T_1$ and $T_2$, and any point, $p\in T_1$, any map, $f:T_1\to T_2$, such that for any neighborhood, $U_{f(p)}$, of $f(p)$, there is a neighborhood, $U_p$, of $p$ such that $f(U_p)\subseteq U_{f(p)}$

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References

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