Welcome to mathimatikoi.org forum; Enjoy your visit here.

## Continuous functions

General Topology
Grigorios Kostakos
Founder
Articles: 0
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.
1. Prove that the set $F=\big\{x\in X\;|\; f(x)=g(x) \big\}$ is closed set of $X$.
2. If $D$ is a dense subset of $X$, such that $f (x) = g(x)$, for every $x\in D$, prove that $f = g$.
Grigorios Kostakos