For each of the following, subsets of R decide whether or not the set has an...

For each of the following, subsets of R decide whether or not the set has an infimum and/or a supremum. If they exist, write down the infimum and supremum, and say whether it is an element of the set. (a) [3,7)

(b) {x ∈ Q : 1 ≤ x < 5}

(c) {1, 2, 3, . . . }

(d) {. . . , 1/4, 1/2, 1, 2, 4, . . . }

Expert Solution

Colby Messinger answered 7 months ago

Let X be the set of all subsets of R whose complement is a finite set...

Let X be the set of all subsets of R whose complement is a finite set in R: X = {O ⊂ R | R − O is finite} ∪ {∅} a) Show that T is a topological structure no R. b) Prove that (R, X) is connected. c) Prove that (R, X) is compact.

For each of these relations on the set {1, 2, 3, 4}, decide whether it is...

For each of these relations on the set {1, 2, 3, 4}, decide whether it is reflexive, whether it is symmetric, whether it is antisymmetric, and whether it is transitive. {(2, 4), (4, 2)} {(1, 2), (2, 3), (3, 4)} {(1, 1), (2, 2), (3, 3), (4, 4)} {(1, 3), (1, 4), (2, 3), (2, 4), (3, 1), (3, 4)} For a) and b) please use the graph representation to determine their properties For c) and d) please use matrix...

Given the following subsets of R: A = R\Q = {x ∈ R|x not in Q}...

Given the following subsets of R: A = R\Q = {x ∈ R|x not in Q} B = {1, 2, 3, 4} C = (0, 1] D = (0, 1] ∪ [2, 3) ∪ (4, 5] ∪ [6, 7] ∪ {8} (a) Find the set of limit points for each subset when considered as subsets of RU (usual topology on R). (b) Find the set of limit points for each subset when considered as subsets of RRR (right-ray topology on...

For the following exercises, find the number of subsets in each given set. {a, b, c, … , z}

For the following exercises, find the number of subsets in each given set.{a, b, c, … , z}

Consider the following collections of subsets of R: B1 ={(a,∞):a∈R}, B2 ={(−∞,a):a∈R}, B3 ={[a,∞):a∈R}, B4 =...

Consider the following collections of subsets of R: B1 ={(a,∞):a∈R}, B2 ={(−∞,a):a∈R}, B3 ={[a,∞):a∈R}, B4 = {[a, b] : a, b ∈ R}, B5 = {[a, b] : a, b ∈ Q}, B6 ={[a,b]:a∈R,b∈Q}. (i) Show that each of these is a basis for a topology on R. (ii) What can you say about the corresponding topologies T1,...,T6, eg, are any of the topologies the same, are any comparable, are any equal to familiar topologies on R, etc?

Consider the following subsets of the set of all students: A = set of all science...

Consider the following subsets of the set of all students: A = set of all science majors B = set of all art majors C = set of all math majors D = set of all female students Using set operations, describe each of the following sets in terms of A, B, C, and D: a) set of all female physics majors b) set of all students majoring in both science and art

Decide for each one of the following decays whether it is possible or not. If not,...

Decide for each one of the following decays whether it is possible or not. If not, point out which law of conservation is violated. Ξ- -> Λo + π- + ν Ξ- -> Ω- + πο Ξ- -> π- + γ A Ξ- particle break down through the process Ξ- -> Λo + π- What can be the type of interaction responsible for the decay? Please reason your answer. Write down an equation with one unknown variable for the momentum...

write a respose to the following question. in each of the following cases, decide whether a...

write a respose to the following question. in each of the following cases, decide whether a biomial distributio is an appropriate modddule and give your reason. 1. a firm uses a computer based training module to prepare 20 machinists to use new numerically controlled lathes. the module contains a test at the end of the course, x is the number who perform satisfactory on the test. 2. the list of potential product testers for a new product contains 100 person...

For each of the following vector fields F, decide whether it is conservative or not by...

For each of the following vector fields F, decide whether it is conservative or not by computing curl F. Type in a potential function f (that is, ∇f=F). Assume the potential function has a value of zero at the origin. If the vector field is not conservative, type N. A. F(x,y)=(−14x−6y)i+(−6x+6y)j f(x,y)= C. F(x,y,z)=−7xi−6yj+k f(x,y,z)= D. F(x,y)=(−7siny)i+(−12y−7xcosy)j f(x,y)= E. F(x,y,z)=−7x^2i−6y^2j+3z^2k f(x,y,z)=

For each of the following vector fields F , decide whether it is conservative or not...

For each of the following vector fields F , decide whether it is conservative or not by computing curl F . Type in a potential function f (that is, ∇f=F). If it is not conservative, type N. A. F(x,y)=(10x+7y)i+(7x+10y)jF(x,y)=(10x+7y)i+(7x+10y)j f(x,y)=f(x,y)= B. F(x,y)=5yi+6xjF(x,y)=5yi+6xj f(x,y)=f(x,y)= C. F(x,y,z)=5xi+6yj+kF(x,y,z)=5xi+6yj+k f(x,y,z)=f(x,y,z)= D. F(x,y)=(5siny)i+(14y+5xcosy)jF(x,y)=(5sin⁡y)i+(14y+5xcos⁡y)j f(x,y)=f(x,y)= E. F(x,y,z)=5x2i+7y2j+5z2k

Question