The closare of a set is smallest closed set containing s صواب ihi

Q: If  X is a countable set show that every topology on X is second countable.

A: To Show: If  X is a countable set show that every topology on X is second countable.

Q: In the discrete topology on the set X, every set is open and it also follows that every set is…

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Q: 4- A subset [a, b] R is compact set in: a- (R, Td), b- (R, T), c-Both (R, Tu) and (R, T₁) d- No one.…

A: As per our guidelines we are supposed to answer only first part. Kindly repost other parts in the…

Q: Give an example of a set in R ^ 2 with the usual topology that is not connected but has a connected…

A: Let's examine the  problem for path-connectedness example of a set in R2 with the usual topology…

Q: Argue that a set A is a Gδ set if and only if its complement isan Fσ set.

A: The given statement is of Baire’s Theorem.

Q: Let B be a set and {A: aeA} be an arbitrary family of sets. Then BUn A) = %3D

A: Answer

Q: An indexed family of sets (Alhet is said to be a cover of a set X if and only if X CUieIA . Use this…

A: It  has been given to us that  X⊆∪i∈I{C}i and X⊆∪j∈J{D}j. We need to show that X⊆∪(i,j)∈I×J{Ci∩Dj} .…

Q: True or False If A is a set, the complement of A is the setof all the elements in the universal set…

A: Complement of a set A: Consider a set A. Then the complement of the set A is the set of all elements…

Q: 3.1 Show that a finite intersection of closed sets is closed.

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Q: (b) Show that the continuous image of compact set is compact but the convers need not to be true.…

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Q: Prove that ifS is a bounded set, then inf(S) = -sup(-S) %3D

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Q: Show

A: We prove this statement by using definition of Borel Set.

Q: Let A be a bounded non-empty set. Then inf A < sup A. True False

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Q: Show that every open set with respect to 7 is a union of open ball(s).

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Q: Give an Such that. example of sets A andB

A: Universal Set: We consider all the sets to be the subsets of a given set known as the universal set…

Q: Define Closed sets ?

A: Closed sets are defined as a set which consists all of their limits points. It is also defined as…

Q: Elements that are in the universal set but not in the set A, are members of the set called, of A.…

A: Universal set : Any set that contains all the sets is called Universal set Subset:  All the elements…

Q: Suppose that X is a set and {A. : a E I} is an indexed family of sets (which contains at least one…

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Q: Prove that (2,5) is an open set

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Q: 3. is in the span of the set { -1 Birini seçin: O Doğru O Yanlış

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Q: Prove that empty set is subset of all sets: φ ⊆ A

A: Given: An empty set and set A is given. To Find: To prove that empty set is subset of all sets: ϕ⊆A

Q: Show that the o-algebra B of Borel sets contains all F,-sets.

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Q: Call a set A CR clopen if it is both open and closed. Prove that the only clopen sets are Ø and R.

A: A⊆R clopen if it is both open and closed.  We have to prove that the only clopen sets are ϕ and R

Q: Is the Cantor set closed? Is it compact? Explain!

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Q: Give an example of a closed set in R ^ 3 with the usual topology that is not compact

A: Given the usual topology on ℝ3. i.e. τusual=U⊆ℝ3: ∀x∈U, ∃∈&gt;0 such that B∈x⊆U

Q: Use the definition of compact set to prove that the set [0,1] is compact

A: We know that a set E is compact if every open cover of E has a finite subcover. We suppose, that O…

Q: two example of open set in R, closed set in R, and the closure of that set

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Q: Let X be an infinite set, then any topology on X is also infinite. Select one: O True O False

A: Note: " Since you have asked multiple question. As per our guidelines we are supposed to solve only…

Q: If {A;}je1; where A; is bounded set for each indexed i, I any indexed set then Ujel A¡ is no…

A: Answer is we can't say  No decision.

Q: Prove that derived set of a bounded set is also bounded.

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Q: let to be anonempty subset of abounded set E-Show that infESinf to Ssup E ssup E

A: Given :  E0 is a non empty subset of a bounded set E. To show :  inf E ≤ inf E0 ≤sup E0 ≤ sup E

Q: Show that any subset of bounded set is bounded

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Q: open

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Q: Prove that empty set is subset of all sets: φ ⊆ A     Please help me figure this question out.

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Q: Give a set that is not closed under addition

A: In the question we have to give a set that is not closed under addition.

Q: Construct a family of sets that demonstrates R is not compact

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Q: disprove the following AUB s connected set then either A set prove on or B is conniedted

A: Since it is a multiple questions. As per our company guidelines, we have to solve the first one. For…

Q: Let X be a nonempty set with subsets, A, B, and C. Prove that A ∩ (B \ C) = (A ∩ B) \ (A ∩ B).

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Q: 5. If X any Y are sets, then X-Y {r€X: z4Y} If X is open set and Y is closed set. Prove that (a) X-Y…

A: Let X is open set and Y is closed set

Q: Let A1,A2,.......,An be countable sets. Prove that  A1 x A2 x.............An = { a1, a2,…

A: Let A1,A2,.......,An be countable sets. Then we have to show that    A1 x A2 x.............An = {…

Q: Give an example of a set in R ^ 2 with the usual topology that does not have any subset (not…

A: Given that R2 with the usual topology. The aim is to find an example of the set  R2 with the usual…

Q: Prove that every set with positive Lebesgue measure contain a non-measurable set

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Q: It is a set denoted by and contains those elements that belong to both A and B.a. Complement of the…

A: In this case, we need to identify the correct option for the given statement.

Q: An indexed family of sets (A,hcs is said to be a cover of a set X if and only if X CU,crA Use this…

A: Let A be a non-empty set and Cii∈I and Djj∈J are two different covers of A. Since Cii∈I is cover of…

Q: 2. Let A be nonempty set. Show that if A is infinite set, then A x {a} is infinite set

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Q: Prove that the set of all finite subsets of ω is countable. (Set theory)

A: The objective is to prove that the set of all finite subsets of ω is countable.

Q: 2- Moke the definitions of open and closed sets. x =Larbic,d,eļ and ノ closed subsets of (x,T) space,…

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