Mathematics · Topology
Let U = {x ∈ &mathbb{Q} : 0 ≤ x ≤ 1} and V = {x ∈ &mathbb{Q} : 0 < x < 2} be subspaces of the rational numbers &mathbb{Q} with the subspace topology inherited from &mathbb{R}. Let m and n be the number of connected components of U and V, respectively. Then:
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- 1m = 2n, where m, n are finite
- 2both m and n are countably infinite✓
- 3m = n = 1
- 4m > 2n, where m, n are finite
Correct answer
both m and n are countably infinite
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