Chapter 12: Q. 6 (page 985)

What is meant by a “closed” subset of $ℝ^{2}$ ? What is meant by a “bounded” subset of $ℝ^{2}$ ?

Short Answer

Expert verified

A subset $S$ of $ℝ^{2}$ is said to be closed if its complement, $S^{c}$ , is open.

A subset $A$ of $ℝ^{2}$ is said to be bounded if $A$ is a subset of some open disk $D$ in $ℝ^{2}$ .

Step by step solution

Step 1. Given information

We need to write the definition for “closed” and "bounded" subset of $ℝ^{2}$ .

Step 2. Explanation for the bounded and the closed subset of ℝ2:

A subset $S$ of $ℝ^{2}$ is said to be closed if its complement, $S^{c}$ , is open. A subset $A$ of $ℝ^{2}$ is said to be bounded if $A$ is a subset of some open disk $D$ in $ℝ^{2}$ .

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What is meant by a “closed” subset of $ℝ^{2}$ ? What is meant by a “bounded” subset of $ℝ^{2}$ ?

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation for the bounded and the closed subset of ℝ2:

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What is meant by a “closed” subset of ℝ2? What is meant by a “bounded” subset of ℝ2?

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation for the bounded and the closed subset of ℝ2:

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

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What is meant by a “closed” subset of $ℝ^{2}$ ? What is meant by a “bounded” subset of $ℝ^{2}$ ?