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content/Math4201/Math4201_L10.md
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# Math4201 Lecture 10
# Math4201 Topology I (Lecture 10)
## Continuity
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Let $X,Y$ be topological spaces and $f:X\to Y$. For any $x\in X$ and any open neighborhood $V$ of $f(x)$ in $Y$, $f^{-1}(V)$ contains an open neighborhood of $x$ in $X$.
#### Lemma for continuous functions
Let $f:X\to Y$ be a function, then: