If (X, d1) and (Y, d2) are two metric spaces, then a function f : X → Y is continuous if and only if:

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Mathematics · Real Analysis

Verified Solution4 OptionsUpdated: October 2026👁️1 View

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for each closed set H ⊆ Y, f-1(H) is a closed subset of X.

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Answer 1

for each open set H ⊆ Y, f-1(H) is a closed subset of X.

Answer 2

for each closed set H ⊆ Y, f-1(H) is a closed subset of X.

Answer 3

for each closed set H ⊆ Y, f-1(H) is an open subset of X.

Answer 4

for each closed set H ⊆ Y, f-1(H) is neither open nor closed in X.

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