Mathematics · Topology
Let (X, d1) and (Y, d2) be metric spaces. A function f: X → Y is continuous if and only if:
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1for each open set H ⊂ Y, f-1(H) is a closed subset of X
- 2for each closed set H ⊂ Y, f-1(H) is a closed subset of X✓
- 3for each open set H ⊂ Y, f-1(H) is neither open nor closed in X
- 4for each closed set H ⊂ Y, f-1(H) is an open subset of X
Correct answer
for each closed set H ⊂ Y, f-1(H) is a closed subset of X
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