Mathematics · Metric Spaces

In any metric space (X, d), which of the following functions is always continuous?

Verified Solution4 OptionsUpdated: October 2026👁️1 View

1The indicator function of a subset
2The distance function d(x, y)✓
3The constant-valued discontinuous step function
4Every arbitrary bounded function

Correct answer

The distance function d(x, y)

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In any metric space (X, d), which of the following functions is always continuous?

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