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Answer :
Final answer:
If XxY is compact, then both X and Y are compact.
Explanation:
To determine if X and Y are compact when XxY is compact, we need to consider the properties of the projection function. The projection function maps elements of the product space XxY to the individual spaces X and Y.
The fact states that the projection function is continuous, open, and onto. This means that the projection function preserves the compactness of the product space.
If XxY is compact, it implies that the projection function is continuous, open, and onto. Therefore, both X and Y are also compact.
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