Physics · Topology
Let (X, d1) and (Y, d2) be metric spaces. If f: (X, d1) → (Y, d2) is a continuous function, then which of the following statements is NOT always true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1For any B ⊆ Y, f-1(B°) ⊆ (f-1(B))°, where B° denotes the interior of B.
- 2For any B ⊆ Y, cl(f-1(B)) ⊆ f-1(cl(B)), where cl(B) is the closure of B.
- 3For any A ⊆ X, f(cl(A)) ⊆ cl(f(A)), where cl(A) is the closure of A.
- 4For any A ⊆ X, f(A°) ⊆ (f(A))°, where A° denotes the interior of A.✓
Correct answer
For any A ⊆ X, f(A°) ⊆ (f(A))°, where A° denotes the interior of A.
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