1. a) Let (x, d) be a metric space. Define a flow on (x, d). b) Let (x, {ϕt}) be a flow on a metric space X. When is xo in x a fixed point of the flow? c) When do you say that a fixed point xo in x is Poincare stable? d) When do you say that a fixed point xo is Lypanov stable?

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A: First, we will find the equation of a line given two points.

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A: The objective of the question is to define a flow on a metric space, identify a fixed point of the…

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A: the usual metric d(x,y)=|x-y| usually induces the norm.

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Q: Q. Let (X, B(R), µ) be a Borel measure space. If AnB=¢, BnC = 0, u(AnC) = 0. Determine µ(AUBUC).

A: Measure theory

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Q: d set): Let (M ,d) be a (SUT)' = S' U T'.

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Q: Material

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A: Let us prove above result

Q: r', where i =

A: As per rule, allowed to answer first question and post the remaining in the next submisison.

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