e al HIIL equ U VILII the discrete topology T, then (X,T) is compact. * O True O False <>

Q: Set roster notation of U={r € Z l -2<r<2

A: we have given the set U = {r∈Z,  -2&lt;r&lt;2} we have to write the set roster notation of U The set…

Q: Let I be the set of real numbers equipped with the standard topology. Let A and B be two subsets of…

A:

Q: * Let R be with the indiscrete topology. If A = {1,3, 5, 7, . }, then A' = A O N O RO

A: This question is related to topology, we will use the definition of indiscrete topology to solve it.

Q: 13. The interior of a set coincides with the interior of its closure..

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let R be equipped with the Euclidean topology T and let Y =]10,20[. We denote by Ty the induced…

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Give ane example of each of the tollowng. Also justif your choice of exxample (i) A self adgoint…

A:

Q: Which one of the following statements is true? * R with the Euclidean topology and R with the finite…

A: Answer

Q: Which one of the following statements is true?

A: As in R with euclidean and R with finite closed topology then function f may not be continuous, thus…

Q: sume transitivity holds, and let A, B, and C be three bundles. Then, if A is preferred to B and B is…

A: Relexivity implies A is preferred to A.  Therefore option  reflexivity implies that A is preferred…

Q: Let A = {a, b, c, d} and let R = {(a, a), (a, b), (a, c), (a, d), (b, b), (b, c), (b, d), (c, c),…

A:

Q: QLet (X,t) be a topological space and A,E are two subsets of x show that : 3. A is closed set iff A…

A:

Q: al let (xt) betopology space and BCY then B is closed in y iff there is closed set CinX st B-COY

A: Let (X,Γ) be topology space and B⊂Y To Prove: B is closed in Y iff there is a closed set C in X s.t…

Q: Which one of the following statements is true? * R with the Euclidean topology and R with the…

A: Two homeomorphic spaces share the same Topological property If one of them is compact, then the…

Q: The usuall metric space (Rd)isComplete ***

A:

Q: Ris not connected if T is the trivial (usual) topology O the lower limit topology the indiscrete…

A: We know that

Q: Ris not connected if T is * O None of the choices O the trivial (usual) topology the indiscrete…

A: R is not connected if T is

Q: Let X = {1, 2, 3, 4, 5, 6}. Prove that in general, if X is finite there is only one topology for X…

A: Let X = {1, 2, 3, 4, 5, 6}. Prove that in general, if X is finite there is only one topology for X…

Q: Give an example of sets S and T where P(SUT)メP(S) U P(T)

A: Let, S={3,7} and T={4} be any set and P(SUT) be a power set of union of S and…

Q: Prove that if X∩Y = X∩Z and X∪Y = X∪Z, then Y = Z for all sets X,Y, and Z.

A:

Q: Question 2* Which one of the followings is compact a. A discrete space with at least to points. b.…

A: Given: Statements: (a) A discrete space with at least two points is compact. (b) Any set with the…

Q: Which one of the following statements is true?* R with the Euclidean topology and R with the…

A: Which one of the following statement is true

Q: Suppose X has the discrete topology. Then the infinite product X with the product topology is also…

A: It is given that X has the discrete topology. Check whether the infinite product Xw with product…

Q: Q Let X be an Infinite sel with topdogy ?. Prove or disprove : (a) If every mfinite Suhsel of x i…

A: