Can anyone provide any ideas or hints for this problem?(adsbygoogle = window.adsbygoogle || []).push({});

Let f:R^2 -> R satisfy the following properties:

- For each fixedx, the function y -> f(x,y) is continuous.

- For each fixedy, the function x -> f(x,y) is continuous.

- If K is a compact subset of R^2, then f(K) is compact.

Prove that f is continuous.

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# Homework Help: Challenging Compactness/Continuity Problem

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