Chapter 12: Q. 1 (page 988)

Fill in the blanks to complete each of the following theorem statements:
If $S$ is a closed subset of $ℝ^{3}$ , then $S^{c}$ is _____ subset of $ℝ^{3}$ .

Short Answer

Expert verified

If $S$ is a closed subset of $ℝ^{3}$ , then $S^{c}$ is open subset of $ℝ^{3}$ .

Step by step solution

Step 1. Given information

If $S$ is a closed subset of $ℝ^{3}$ , then $S^{c}$ is _____ subset of $ℝ^{3}$ .

Step 2. Filling in the blanks

If S is a closed subset of $ℝ^{3}$ , then $S^{c}$ is open subset of $ℝ^{3}$ .

By definition, a subset $S$ of $ℝ^{2}$ or $ℝ^{3}$ is said to be closed if its complement, $S^{c}$ , is open subset of $ℝ^{2}$ or $ℝ^{3}$ respectively.

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Fill in the blanks to complete each of the following theorem statements:
If $S$ is a closed subset of $ℝ^{3}$ , then $S^{c}$ is _____ subset of $ℝ^{3}$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Filling in the blanks

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Fill in the blanks to complete each of the following theorem statements:If Sis a closed subset of ℝ3, then Scis _____ subset of ℝ3.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Filling in the blanks

One App. One Place for Learning.

Most popular questions from this chapter

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Fill in the blanks to complete each of the following theorem statements:
If $S$ is a closed subset of $ℝ^{3}$ , then $S^{c}$ is _____ subset of $ℝ^{3}$ .