Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Analysis Metric Spaces
Let (X, d) be a metric space and let A ⊆ X. For x ∈ X, define d(x, A) = inf{d(x, a): a ∈ A}. If d(x, A) = 0 for all x ∈ X, then which of the following assertion must be true?
1
A is compact
2
A is closed
3
A is dense in X
4
A = X