Question

5. Let $(X, d)$ be a metric space. A subset $A \subset X$ is said to be bounded if there exists $r > 0$ and a point $p \in X$ such that $A \subset B_r(p)$. Prove that the union of two bounded sets is also bounded.

Name: 5. Let (X, d) be a metric space. A subset A ⊂ X is said to be bounded if there exists r > 0 and a point p ∈ X such that A ⊂ Br(p). Prove that the union of two bounded sets is also bounded.
Uploaded: 2023-02-10T11:15:07-08:00
Duration: 5 min 29 s
Channel: Madhur L
Description: 5. Let (X, d) be a metric space. A subset A ⊂ X is said to be bounded if there exists r > 0 and a point p ∈ X such that A ⊂ Br(p). Prove that the union of two bounded sets is also bounded.

          5. Let $(X, d)$ be a metric space. A subset $A \subset X$ is said to be bounded if there exists $r > 0$ and a point $p \in X$ such that $A \subset B_r(p)$. Prove that the union of two bounded sets is also bounded.

5. Let (X, d) be a metric space. A subset A ⊂ X is said to be bounded if there exists r > 0 and a point p ∈ X such that A ⊂ Br(p). Prove that the union of two bounded sets is also bounded.

Added by Raymond B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

02/10/2023

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Step 1: Assume A and B are two bounded sets in the metric space (X, d). Show more…

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5. Let (X, d) be a metric space. A subset A ⊆ X is said to be bounded if there exists r > 0 and a point p ∈ X such that A ⊆ Br(p). Prove that the union of two bounded sets is also bounded. 5. Let (X,d be a metric space. A subset A C X is said to be bounded if there exists r > 0 and a point p E X such that A C Br(p). Prove that the union of two bounded scts is also bounded.