Problem 1300 (difficulty: 3/10)

Let \(\displaystyle f:\R^p\to \R^q\), \(\displaystyle A,B\subset \R^p\) be closed. \(\displaystyle f\) is continuous when restricted to either \(\displaystyle A\) or \(\displaystyle B\). Is it true that \(\displaystyle f\) is continuous when restricted to \(\displaystyle A\cup B\)?

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