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I know most of the result regarding Continuity, Completeness. But I got stuck into a question which I found in a question paper. Let $f:X \longrightarrow Y$ Where $X,Y$ metric space.Then show that for any Cauchy sequence $\{x_n\}$ in $X$ if $\{f(x_n)\}$ is Cauchy in $Y$, then $f$ is continuous. Please help me. Thanks in advance.

Ritesh Khan
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  • Statement unclear. I think you are asking to show that, if the sequence $f(x_n)$ is Cauchy in $Y$ for every Cauchy sequence $x_n$ in $X$, then $f$ is continuous. Is that what you mean? – Gerry Myerson May 27 '19 at 02:20

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