Q. 8 What is meant by a 鈥渃losed鈥� ... [FREE SOLUTION]

Chapter 12: Q. 8 (page 985)

What is meant by a 鈥渃losed鈥� subset of ${鈩�}^{3}$ ? What is meant by a 鈥渂ounded鈥� subset of ${鈩�}^{3}$ ?

Short Answer

Expert verified

A subset $S$ of ${鈩�}^{3}$ is said to be closed if its complement, $S^{c}$ , is open. A subset $A$ of ${鈩�}^{3}$ is said to be bounded if $A$ is a subset of some open ball $B$ in ${鈩�}^{3}$ .

Step by step solution

Step 1. Given information

We need to write the definition for 鈥渃losed鈥� and "bounded" subset of ${鈩�}^{3}$ .

Step 2.Explanation for the bounded and the closed subset of ℝ3:

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91影视

What is meant by a 鈥渃losed鈥� subset of ${鈩�}^{3}$ ? What is meant by a 鈥渂ounded鈥� subset of ${鈩�}^{3}$ ?

Short Answer

Step by step solution

Step 1. Given information

Step 2.Explanation for the bounded and the closed subset of ℝ3:

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91影视

What is meant by a 鈥渃losed鈥� subset of 鈩�3? What is meant by a 鈥渂ounded鈥� subset of 鈩�3?

Short Answer

Step by step solution

Step 1. Given information

Step 2.Explanation for the bounded and the closed subset of ℝ3:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Theoretical and Mathematical Physics

Discrete Mathematics

Calculus

Statistics

Geometry

Study anywhere. Anytime. Across all devices.

What is meant by a 鈥渃losed鈥� subset of ${鈩�}^{3}$ ? What is meant by a 鈥渂ounded鈥� subset of ${鈩�}^{3}$ ?