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Definition 3.46. A space X with topology T is said to be a Hausdorff space iff it satisfies the following axiom: (H) V different x, y E X, 3U, V ET, such that r E U Ay E VAUOV = 0. {0, 1, 2} such that X (1) is, Exercise 3.47. Give examples of topologies on the set X and (2) is not, a Hausdorff space. %3D Exercise 3.48. Suppose X has topologies T1 C T2. What does one topology being Hausdorff imply about the other?

Definition 3.46. A space X with topology T is said to be a Hausdorff space iff it satisfies the following axiom: (H) V different x, y E X, 3U, V ET, such that r E U Ay E VAUOV = 0. {0, 1, 2} such that X (1) is, Exercise 3.47. Give examples of topologies on the set X and (2) is not, a Hausdorff space. %3D Exercise 3.48. Suppose X has topologies T1 C T2. What does one topology being Hausdorff imply about the other?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Please solve 3.47 and 3.48 

Definition 3.46. A space X with topology T is said to be a Hausdorff space iff it satisfies the following axiom: (H) V different x, y E X, 3U, V ET, such that x E U ^ y E V UNV = Ø. {0, 1,2} such that X (1) is, Exercise 3.47. Give examples of topologies on the set X and (2) is not, а Наusdor:ff sрасе. 6. Exercise 3.48. Suppose X has topologies T1 C T2. What does one topology being Hausdorff imply about the other?
Transcribed Image Text:Definition 3.46. A space X with topology T is said to be a Hausdorff space iff it satisfies the following axiom: (H) V different x, y E X, 3U, V ET, such that x E U ^ y E V UNV = Ø. {0, 1,2} such that X (1) is, Exercise 3.47. Give examples of topologies on the set X and (2) is not, а Наusdor:ff sрасе. 6. Exercise 3.48. Suppose X has topologies T1 C T2. What does one topology being Hausdorff imply about the other?
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