Question

4. Let $d$ be a distance function defined on the space $X$. Prove that \\ $\min(1, d(x, y))$, $\frac{d(x, y)}{1 + d(x, y)}$, $x, y \in X$. \\ are distance functions. Describe the open sets with respect to these new \\ metrics.

          4. Let $d$ be a distance function defined on the space $X$. Prove that \\
$\min(1, d(x, y))$, $\frac{d(x, y)}{1 + d(x, y)}$, $x, y \in X$. \\
are distance functions. Describe the open sets with respect to these new \\
metrics.

4. Let d be a distance function defined on the space X. Prove that

min(1, d(x, y)), (d(x, y))/(1 + d(x, y)), x, y ∈ X.

are distance functions. Describe the open sets with respect to these new

metrics.

Added by Stephen S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

01/08/2023

Step 1

Step 1: We need to show that min(1,d(x,y)) is a distance function. Show more…

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Let d be a distance function defined on the space X. Prove that min(1,d(x,y)),(d(x,y))/(1+d(x,y)),x,y in X are distance functions. Describe the open sets with respect to these new metrics. 4. Let d be a distance function defined on the space X. Prove that d(x,y) min(1,d(x,y)), c,y in X. 1+d(x,y)' are distance functions. Describe the open sets with respect to these new metrics.