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Chapter 12: Q. 6 (page 985)

What is meant by a 鈥渃losed鈥� subset of 鈩�2? What is meant by a 鈥渂ounded鈥� subset of 鈩�2?

Short Answer

Expert verified

A subset Sof 鈩�2is said to be closed if its complement, Sc, is open.

A subset Aof 鈩�2is said to be bounded if Ais a subset of some open disk Din 鈩�2.

Step by step solution

01

Step 1. Given information

We need to write the definition for 鈥渃losed鈥� and "bounded" subset of 鈩�2.

02

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

A subset Sof 鈩�2is said to be closed if its complement, Sc, is open. A subset Aof 鈩�2is said to be bounded if Ais a subset of some open disk Din 鈩�2.

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