ор (i) [0, 1) × (0, 1]

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Exercise 17 Let X = R² be the plane mit Sorgenfrey product-topologie.
Are the following sets open?
(i) [0, 1) × (0.1] (ii) {(x, y) R²: x + y ≤ 1}.
Describe the relative topology for the following subspaces:
(i) {(x, y) R²: x+y=0} (ii) {(x,y) R²: x=y=0}
(iii) {(x,y) ER²: x² + y² = 1}.
Transcribed Image Text:Exercise 17 Let X = R² be the plane mit Sorgenfrey product-topologie. Are the following sets open? (i) [0, 1) × (0.1] (ii) {(x, y) R²: x + y ≤ 1}. Describe the relative topology for the following subspaces: (i) {(x, y) R²: x+y=0} (ii) {(x,y) R²: x=y=0} (iii) {(x,y) ER²: x² + y² = 1}.
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