Question

Let $f: \mathbb{R}^n \to \mathbb{R}^m$ be a function that is continuous everywhere. Prove that the set $A := \{x \in \mathbb{R}^n \mid ||f(x)|| < 1\}$ is an open set in $\mathbb{R}^n$.

Name: Let f: ℝ^n →ℝ^m be a function that is continuous everywhere. Prove that the set A := {x ∈ℝ^n | ||f(x)|| < 1} is an open set in ℝ^n.
Uploaded: 2023-09-23T05:37:10-08:00
Duration: 2 min 3 s
Channel: Sri K
Description: Let f: ℝ^n →ℝ^m be a function that is continuous everywhere. Prove that the set A := {x ∈ℝ^n | ||f(x)|| < 1} is an open set in ℝ^n.

          Let $f: \mathbb{R}^n \to \mathbb{R}^m$ be a function that is continuous everywhere. Prove that the set $A := \{x \in \mathbb{R}^n \mid ||f(x)|| < 1\}$ is an open set in $\mathbb{R}^n$.

$Let f: ℝ^n →ℝ^m be a function that is continuous everywhere. Prove that the set A := {x ∈ℝ^n | ||f(x)|| < 1} is an open set in ℝ^n.$

Added by Christy L.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

09/23/2023

Step 1

This set consists of all points x in R^n such that the norm of the function f(x) is less than 1. We need to prove that A is an open set in R^n. Show more…

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Let f:R^(n)->R^(m) be a function that is continuous everywhere. Prove that the set A:={xinR^(n)|||f(x)||<1} is an open set in R^(n). Let fRn Rm be a function that is continuous everywhere.Prove that the set A{xER|f1} is an open set in Rn