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Difference between revisions of "Is a constant function always continuous?"
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Latest revision as of 13:15, 14 July 2013
Question: Is a constant function $f:R\rightarrow R$ always continuous?
Answer: Yes.
Why: For a given $\epsilon$ choose arbitrary $\delta$.
If $f:X\rightarrow Y$ is a constant function between two topological spaces, for any neighborhoods $U$ of $a$ and $V$ of $f(a)$, we have $$f(U)=\{f(a)\}\subset V.$$ $\blacksquare$
See Examples of maps.