3\ Let T = {0} U {un, neN} un = numbers N and A = {2,3,5} be {n, n+1, n + 2,...} r is topology on a set of natural a subset of natural numbers find Int(A), b(A), A', and TA

Q: u* (B) = inf{l&l:s is a covering of B by closed boxes} for all BcR" صواب İhi

A:

Q: 2. Prove the general formulas (GF)» = G«F* and (F-')» = (F«)- in the special case where F and G are…

A: Given G and F re isometries in ℝ3 To prove  1.GF*=G*F*2. F-1*=F*-1 Since F and G are isometries in…

Q: IfA =[-3,5] U {6, 7} U [8, 00), then Find each of the following (1) inf (A) (2) sup (A) (3) int (A)…

A: Let A=-3,5∪6,7∪[8,∞). (1) inf A is computed as computed as follows, (-∞,-3) is a lower bound of A.…

Q: Theorem 23. If u, v E Q then we can find integers a, b, d with d > 0 such that u = a and v = d'…

A: By Division Algorithm we know that,               Let a, b be two integers with b>0. Then there…

Q: Theorem: If R is a fuzzy relation on the set X, then (R-1)-1 = R

A:

Q: Prove that (23-1a,b)* = {2}-1/a})(27-1) j=1 for all real numbers a₁,..., an and b₁,..., bn. i=1

A: The detailed process is described in step 2.

Q: Prove that the only idempotent elements in an integral domain R with unity are 0 and 1.

A: Idempotent element : An element a in a ring R is said to be an idempotent element if a.a = a .…

Q: What is Hhe domaind the reratin {(1,l )4,22,4-2), (9,3),(a-23? A-2,3,4,いBこ24,4.8, what id A nB? what…

A:

Q: Use the fundamental theorem of Calculus to solve.

A: Refer to the question we need to calculate the definite integral of the following integrals using…

Q: Find the interval of En=0 2" (z – 3)" O (2.5, 3.5) O (2, 3) ( (3.5, 0) O(2.5, 0)

A:

Q: Let R is ring of real numbers and *, (2) O defind on R^2 as follows, (a, b), (c, d)ER^2 then (a, b)*…

A:

Q: 92+91 Let z be a point that lies on |z| = 2 and f (z) = 243 Then |f(z)| is i2-22+31 O >1 O »3 O None…

A: Given fz=9z+9iiz¯−z2+3i and z be a point that lies on z=2 We have to find the  fz Taking modulus…

Q: Show that the embedding of part (g) takes lines to "lines."

A: (h) We have to show that lines from ℝ2 maps to lines in P2. Lines in ℝ2 will be of the form ax+by=0.…

Q: Find oxthogonal uncdary diagonalizing an or matri'y to lMowing tor One 2 (a) (b) 3 -2 -2

A: A square matrix A is called as orthogonal matrix if AxAT=ATxA=I where AT transpose of matrix A. and…

Q: A subset (a,b) ≤R is T2-space in (R,Tu) * 1 true 2 False

A: Given: A subset (a, b)⊆ℝ is T2-space in ℝ, Tu. To determine: Whether given statement is true or…

Q: 4) Let A SR where A is a finite set. (i) J=the standard topology topology Compute INT (4) when: (ii)…

A:

Q: 12 Let (RTR) is topological Space Such that TR-243 U2GSR=R-G-G is finste} Find buz), Z², Z. z' then…

A: Here given ℝ, Tℝ is a topological space such that Tℝ=ϕ∪G⊂ℝ: ℝ-G=Gc is finite This topology is known…

Q: QUESTION IS ATTACHED  (PLEASE DO PART B ONLY I HAVE COMPLETED PART A ?)

A: 1 B) to show that the particular APs A(1,0) and A(0,1) form a basis for the 2-dimensional vector…

Q: let U and y be bounded sets. if u er i tre M+ (V) ≤M₂ (V) and M^ (U) SM³ (V) 1

A: Given :  U and V are bounded sets with  U⊆ V. To show :  m*(U) ≤ m*V  and  m*U ≤ m*V,  where m*U and…

Q: Prove that the function f(x1,x2) = In (e*i+= + eV=i+1) is convex over R².

A:

Q: Let (X, T) be a topological space, AcX, then A'next (A) = 10 AO

A:

Q: metoix space and d[211?(₂) for all ₁2 ER 2,12₂ 17. (*/ 1²(₂) d is matrie X. let (Xid) be d' XXR…

A:

Q: ~ on T by (x1, y1, Z1) Let T 3D {(x, у, г) € R'| (х, у, 2) # (0, 0, 0)}. Define ~ on T by (х1, У1,…

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: Consider the topology T on X= (a, b, c, d, e), (X, Ø, (a), (e,d}, {a, e, d), (b, c, d, e}} Show that…

A: It is given that,  X = {a, b, c, d, e} and  T = X, ∅, a, c, d, a, c, d, b, c, d, e be a topology on…

Q: tan u-tan v Prove tan( u – v) = 1+ tan u tan v

A: tanu-v=sinu-vcosu-v=sinucosv-cosusinvcosucosv+sinusinv     ∵sinx-y=sinxcosy-cosxsiny &…

Q: prove that integer V intgers is an

A:

Q: Q2. Answer as true or false: (a) f-'((AUB)nC) = (ƒ-'(A)n f-1C)) U (f-1(B) n f-1(C)). (b) Given the…

A: (a) is True. (b) is False.

Q: Let x ∈ R ^n and r > 0. Is the set B(x, r) = {y ∈ R^ n : ||y − x|| ≤ r} a closed set in R ^n? Y/N

A:

Q: let A be a set. A:=(a1,a2,a3) in R^3 such that a1 is greater than 0 but less than and equals to 1,…

A:

Q: OR SECTION 13.6 1. Let S be a nonempty, closed, convex set in R" that does not contain the origin.…

A: Consider the provided question,   Suppose, S be a non empty, closed, convex set in  that doesn't…

Q: |U( Z Ð Z O Z O Z)| is: O 2 O 16 8

A: We have to determine the number of units in the given algebraic structure.

Q: A Moving to the next question prevents changes to this answer. Question 2 Let AcR be bounded and set…

A: Choose the correct

Q: 13. Let X be a set, let (Y, Ty) be a topological space, and let f: X→Y be a function between sets.…

A: We shall show that tau is a topology in the given space. Please check the next step for details.

Q: 1. Determine all the numbers) of Mean Value Theorem For h Cz) =473 -822t 72-2 on [ 2,5] cwhich…

A:

Q: Ix-yl 1 + |x-yl ₁ = R₁ d (x,y) = R is matric space

A:

Q: - LITALY. PULSI (3) Let N be a set of natural numbers and T={Ø,N}U{U; NEN}. Un={0,1,...,n} show that…

A:

Q: Discuss the two versions of the fundamental theorem of calculus

A: This the problem of Real Analysis, Theory of Reimann Integration.