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Chapter 12: Q 71. (page 932)

Prove that R2 is both an open subset and a closed subset of R2.

Short Answer

Expert verified

It is proved that the aR2 is both an open subset and a closed subset ofR2.

Step by step solution

01

Step 1. Given information. 

We have given set isR2.

02

 Prove the given statement.  

A subset is said to be open if it does not have a boundary to identify.

The given set is a universal set. It involves all the points in the space of R2. It does not have any boundary to identify. So, it is an open set.
The complement of R2is an empty set, which is both open and closed set.
Thus, a R2is Both Open and Closed Set

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