Kokoteksti
Analysis IV Exercise 4 2004
1. The problem 1 of Exercise 3.
2. Prove that the collection of disjoint (pistevieras) open sets in Rn is either finite or countable.
3. Suppose thatf :Rm →Rn is continuous. Prove that f(A)⊂f(A)for all A⊂ Rm. Give an example where f(A)6=f(A).
4. Letf be a continuous real function on a metric space X. Let Z(f) be the set of all p∈X at whichf(p) = 0. Prove that Z(f) is closed.
5. LetA ⊂R and B ⊂Rsuch that A⊂B. Prove that m∗(A)≤m∗(B).
6. Prove Corollary 2.4.
LIITTYVÄT TIEDOSTOT
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We proceed to prove that (11.4) holds outside of E for all r
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Complex analysis Demonstration
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Although corrupt, Muslim scholars have searched, in different degrees, in these Scriptures for certain issues either to prove the correctness of the Qurʾān or to prove the wrongness
The half-space z > 0 is the air and the half-space z < 0 is the earth, whose per- meability is µ 0 and in which there are only Ohmic currents (constant conductivity σ). Prove
