Let ( a 1 , a 2 , . . . , a n )...

Izabella Ponce

Izabella Ponce

Answered

2022-06-24

Let ( a 1 , a 2 , . . . , a n ) R n and b R. Prove that the set:
F 1 := { ( x 1 , x 2 , . . . , x n ) R n | i = 1 n a i x i b }
is closed in R n

Answer & Explanation

Ryan Newman

Ryan Newman

Expert

2022-06-25Added 26 answers

First prove that if f ( x ) : R n R is continuous then the set { x R n | f ( x ) b } is closed in R n . So let f ( x 1 , x 2 , . . x n ) = i = 1 n a i x i . If h , k be to function which are continuous then h + k is continuous. so it is enough to show that f ( x ) = a x is continuous which is obvious ( δ ϵ | a | )

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