Mathematics · Topology
Let X and Y be topological spaces. Consider the statement S: 'For every open subset U ⊆ X × Y and every x ∈ X such that {x} × Y ⊆ U, there exists a neighbourhood W of x in X such that W × Y ⊆ U.' Which of the following conditions guarantees that statement S is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1If Y is compact✓
- 2If X × Y is regular
- 3If Y is connected
- 4If X × Y is Hausdorff
Correct answer
If Y is compact
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