Open/closed sets, limit points, closure, interior
Why this is asked: Sets can be both open and closed, or neither. Know which operations preserve openness (arbitrary unions, finite intersections) and the standard ℚ examples.
Open and closed sets, closure, interior, boundary
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The trap here
“An arbitrary intersection of open sets is open” — false
∩, 1/n) = {0}
Only finite intersections preserve openness.
Check yourself — select all that apply
Let . Which of the following always hold?
Next: Compactness: open covers, sequential, Heine–Borel
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Open this in the full syllabus view · Unit 1