M6140 Topology Exercises - 9th Week (2022)
1 The One-Point Compactification
Exercise 1. What is the one-point compactification of a compact Hausdorff space?
Exercise 2. What is the one-point compactification of Rn?
Exercise 3. What is the one-point compactification of (−2, −1) ∪ (1, 2)?
Exercise 4. What is the one-point compactification of {(x, y) ∈ R2 | 1 < x2 + y2 < 2}?
Exercise 5. What is the one-point compactification of {(x, y) ∈ R2 | x, y ∈ [−1, 1], |xy| < 1}?
Exercise 6. What is the one-point compactification of {(x, y) ∈ R2 | x ∈ [−1, 1]}?
Exercise 7. What is the one-point compactification of R2 \ {(0, 0)}?
Exercise 8. What is the one-point compactification of N?
Exercise 9. What is the one-point compactification of
N
(0, 1)?
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