- Prove that the set $F=\big\{x\in X\;|\; f(x)=g(x) \big\}$ is closed set of $X$.
- If $D$ is a dense subset of $X$, such that $f (x) = g(x)$, for every $x\in D$, prove that $f = g$.

## Continuous functions

- Grigorios Kostakos
- Founder
**Posts:**460**Joined:**Mon Nov 09, 2015 1:36 am**Location:**Ioannina, Greece

### Continuous functions

Let $(X,\rho)$, $(Y,d)$ two metric spaces and $f,g:X\longrightarrow Y$ two continuous functions.

Grigorios Kostakos

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