Prove that (R", II-|) is complete metric space.

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Q: Q7: Prove that (R", |l-|| ) is complete metric space.

A: This is a problem of Topology, Functional Analysis.

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Q: Exercise Prove that: 1. (R, J- |) is a complete metric space. 2. (Q. I-1) is not complete metric…

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A: Let (R,d) be diserete metric space then R is not compact . True or false.??

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A: Answer is mentioned below

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Q: (a) Prove that every finite subset of a metric space is closed and has umulation points.

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Q: (K", || |,) is called the LP-norm on K". is a normed linear space for 1 <PS00. || |,

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Q: give example is not To-SPace about to folegical SPace

A: We have to find a topological space which is not t0.

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Q: 3) Consider the topology ↑ {GCR: 0 ¢ G or G = R} on R. Is open = %3D interval (-1, 1) compact in (R,…

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Q: Show that close ball Y in a metfic space (X,d) is a closed set also show that if (X,d) is complete…

A: Show that closed ball Y in a metric space (X,d) is a closed set also show that if (X,d) is complete…

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Q: let X be a firite dimensional notm Space Then Prove that is compat.

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Q: Q7: Prove that ( IR", ||·|| ) is complete metric space.

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Q: every finite subset of metric space is compact. ture or false?

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Q: Let (R, d) be discrete metric space, then R is not separ able O True O False

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Q: ": Prove that ( R", ||||) is complete metric space.

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A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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Q: Prove that a normed linear space is complete if its unit sphere is complete.

A: We prove that a normed linear space is complete if its unit sphere is complete. Its straightforward…

Q: Give the definition of a separable metric space (S, d). Show that the metric space (IR, d), where…

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