Problem & (3 points). Complete the definition of a metric space by filling in the three blanks: A metric space is a pair (S, d) where S is a set and d: → [0,00) is a function such that

only f.) and g.)

D. Consider R³ with the metric i. Verify that d is really a metric. ii. State and prove the Bolzano-Weierstrass Theorem for R³ with this metric. Hint: Examine the proof for the complex numbers! d((x1, x2, x3), (V1, V2, y3) = |x1-y₁| + x2 - y2 + x3 - y3|.

段階的に解決し、 人工知能を使用せず、 優れた仕事を行います ご支援ありがとうございました SOLVE STEP BY STEP IN DIGITAL FORMAT DON'T USE AI DON'T USE AI DON'T USE AI DON'T USE AI 4. Find a base and the Range for the space generated by: V₁= (1,-2,0,0,3) V₂=(2,-5,-3,-2,6) V3 (0.5,15,10,0) V4 (2,6,18,86)