(d) Let (Fn) be a sequence of closed subsets of M, and S, (j = 1,...,5) be subsets of M such that. S₁ F₁ S₂ = U_F₁ S3 = Sg. MEN nEN Also, S4 has a boundary point a such that a € S, and every convergent sequence in S5 has its limit in S5. Which of the sets S₁,..., S5 are closed.
(d) Let (Fn) be a sequence of closed subsets of M, and S, (j = 1,...,5) be subsets of M such that. S₁ F₁ S₂ = U_F₁ S3 = Sg. MEN nEN Also, S4 has a boundary point a such that a € S, and every convergent sequence in S5 has its limit in S5. Which of the sets S₁,..., S5 are closed.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
please do d) , e) , f) and g)
![(a) Give the centre e and the radius r of S = B(0,5) B(3, 4).
(b) Which of the following are neither open nor closed subsets of Y = (0,7].
V₁ = (0,2], V₂ = [5,7), V3 = (4, 7], V₁ = (3,6], V₁ = (2,17/2).
(c) Let M = R. Using interval notation, give a simplified expression for the set
L = [B(3, 1) UB(7,1)] n B(5,2).
(d) Let (F₂) be a sequence of closed subsets of M, and S; (j = 1,...,5) be subsets of M such that.
S₁ F S₂ = U_Fn S3 = Sg.
NEN*
TEN.
Also, S4 has a boundary point a such that a € S, and every convergent sequence in S5 has its
limit in S5. Which of the sets S₁,..., S5 are closed.
(f) Let F = {x € R: x - 3| < 7 and x + 1 ≥ 2}. Give explicitly F, and F
(g) Let An = [2 + (−1)”+7, 5 + (−1)”+4), n = N*. Set B₂ = An
B
(e) Let u = (2, 2), o = = (0,0) be points in M = R². Let P = (1,6) be a point lying on S(u, 1) and on
the boundary of B(0,r) in R2, for some r > 0. Independently of b, give a numeric value for r.
An+1. Give explicitly An, Bn, and
(h) Suppose that (M, d) is a discrete metric space and a € M. Give a simplified and explicit expression
for: E₁ = B(a, 1/3), E2 = B(a, 1/3), E3 = [S(a, 1)]º, and E4 = S(a, 1).
(i) Give the formal definition in terms of 8 and of the continuity of f: M→ M at ro € M.
(j) Suppose that (M, d) is a discrete metric space. Give the general form of a convergent sequence
(an) in M whose limit is 2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc644c104-f4a0-414b-a375-6de2649477f6%2F9f4558bc-a46c-4625-87da-7fdb53aee81d%2F1wb5cj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) Give the centre e and the radius r of S = B(0,5) B(3, 4).
(b) Which of the following are neither open nor closed subsets of Y = (0,7].
V₁ = (0,2], V₂ = [5,7), V3 = (4, 7], V₁ = (3,6], V₁ = (2,17/2).
(c) Let M = R. Using interval notation, give a simplified expression for the set
L = [B(3, 1) UB(7,1)] n B(5,2).
(d) Let (F₂) be a sequence of closed subsets of M, and S; (j = 1,...,5) be subsets of M such that.
S₁ F S₂ = U_Fn S3 = Sg.
NEN*
TEN.
Also, S4 has a boundary point a such that a € S, and every convergent sequence in S5 has its
limit in S5. Which of the sets S₁,..., S5 are closed.
(f) Let F = {x € R: x - 3| < 7 and x + 1 ≥ 2}. Give explicitly F, and F
(g) Let An = [2 + (−1)”+7, 5 + (−1)”+4), n = N*. Set B₂ = An
B
(e) Let u = (2, 2), o = = (0,0) be points in M = R². Let P = (1,6) be a point lying on S(u, 1) and on
the boundary of B(0,r) in R2, for some r > 0. Independently of b, give a numeric value for r.
An+1. Give explicitly An, Bn, and
(h) Suppose that (M, d) is a discrete metric space and a € M. Give a simplified and explicit expression
for: E₁ = B(a, 1/3), E2 = B(a, 1/3), E3 = [S(a, 1)]º, and E4 = S(a, 1).
(i) Give the formal definition in terms of 8 and of the continuity of f: M→ M at ro € M.
(j) Suppose that (M, d) is a discrete metric space. Give the general form of a convergent sequence
(an) in M whose limit is 2.
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