Mathematics · Topology
Which of the following statements is correct regarding bases for topologies on ℜ2?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1The set of line segments (without endpoints) parallel to the Y-axis forms a basis for the usual Euclidean topology on ℜ2.
- 2The set of open rectangles is a basis for the usual (Euclidean) topology on ℜ2.✓
- 3The set of lines parallel to the Y-axis is a basis for the dictionary order topology on ℜ2.
- 4The set of open right half-planes is a basis for the usual (Euclidean) topology on ℜ2.
Correct answer
The set of open rectangles is a basis for the usual (Euclidean) topology on ℜ2.
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