Continuous functions

General Topology
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Grigorios Kostakos
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Joined: Mon Nov 09, 2015 1:36 am
Location: Ioannina, Greece

Continuous functions


Post by Grigorios Kostakos »

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
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