Any two closed intervals has the different cardinality

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: The Venn diagram here shows the cardinality of each set. Use this to find the cardinality of the…

A: Given data: The given Venn diagram. The expression for the region of Ac is,

Q: Do the sets [0, 1] and [0, 1/2) ∪ (1/2, 1] have the same cardinality? Either give an explicit…

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Q: Thoorem: is not closed set

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Q: Suppose f function between infinite sets A and B, f is not onto function, does the sets A and B have…

A: Yes. It is possible that A and B have same cardinality. Let A and B both are the set of natural…

Q: What is an example of two equivalent sets with the same cardinality BUT DO NOT HAVE a one-to-one…

A: Take A as, 1,2,3 and B as 3,4,5 The cardinality of A and B is 3. Now let's define a function.

Q: Which set has higher cardinality: N or Z? Explain with example

A: Cardinality: The cardinality of a set A is the number of elements present in the set A. We denote…

Q: Suppose S is a set with cardinality n. What is the cardinality of the power set of S ? Are there any…

A: Suppose S is a set with cardinality n. Then power set of S contains 2n elements . Power set of any…

Q: How to prove that the cardinality of the Cantor Set is equivalent to the cardinality of the set of…

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Q: Let A be the set of even positive integers less than 40 and divisible by 4. What is the cardinality?

A: This is the question from set theory.

Q: Let A = {distinct letters occurring in the word HIPPOPOTAMUS}. What is |A|, the cardinality of the…

A: Cardinality of a set is defined as the number of distinct element in that set.

Q: Prove a neighborhood is an open set

A: Recall that, a neighbourhood of a point is a set of points containing that point where one can move…

Q: Let X be finite set with cardinality=n. Prove that the power set P(X) has cardinality 2^n

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Q: Let X be a set and P(X) its power set. Explain what it means that the cardinality of P(X) is…

A: It is required to explain the meaning and to prove that the cardinality of power set P(x), of X, is…

Q: Give example open set is compact

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

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Q: Show that the two given sets have equal cardinality by describing a bijection from one to the other.…

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Q: Use the definition of two sets have the same cardinality to prove that interval (0,2] has the same…

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Q: There are infinitely many different infinite cardinalities.

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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: Show that the two given sets have equal cardinality by describing a bijection from one to the other.…

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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, ∃∈>0 such that B∈x⊆U

Q: The continuous image of a connected set is connected. That is, if X is connected and f : X–→ Y is…

A: We prove this via contradiction. We assume that f(X) is not connected then X is not connected. And…

Q: 4. Prove that the cardinality of the natural numbers is strictly less that the cardinality of the…

A: "According to Bartleby  guideline, Handwritten solutions are not provided" To prove that the…

Q: Show that any convex open set is simply connected.

A: The objective is to prove that any convex open set is simply connected. Simply connected is nothing…

Q: Find a topology in which the point x = 5 is an open set.

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Q: (a) What is the cardinality of the interval (0, 1), finite, countably infinite, or uncountable? (b)…

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Q: union of a collectionm of connected sets that have a point in common is conne

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Q: Show that the Cantor Set contains no open intervals

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Q: If G(sub alpha) is a collection of closed sets, then the intersections of the G(sub alphas) is a…

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Q: The Cantor set is formed by starting with the interval [0,1] and removing the middle third, then…

A: It is given that Cantor set is formed by starting with the interval 0,1 and removing the middle…

Q: The Cartesian product of two sets containing five elements each has a cardinality of * O 16 Cannot…

A: Consider the given two sets which have each cardinality 5 Let set A=a,b,c,d,e and B=1,2,3,4,5

Q: i) show that a closed interval is a closed set;

A: Note: According to bartleby we have to do only first question please upload the question separately.…

Q: Give the cardinality of the set. (If the set has cardinality ℵ0, enter ALEPH NULL.) {1/2, 1/3, 1/4,…

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Q: Give the cardinality of the set. (If the set has cardinality ℵ0, enter ALEPH NULL.) {16, 20, 24, .…

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Q: Suppose we modify the construction of the Cantor set by starting with the open interval (0, 1) and…

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Q: Show that any subset of bounded set is bounded

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Q: Is it possible for two nonempty sets to have the same intersec-tion and union? If so, give an…

A: When two sets A and B overlap that is A = B, then the intersection and union of the  sets A and B…

Q: of the followings are correct about the cardinality of the domain, codomain and range of a function?…

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Q: The union of a infinite number of closed set need not be a Closed set Open Set Both open and close…

A: The union of infinite number of closed sets is

Q: Show that the two given sets have equal cardinality by describing a bijection from one to the other.…

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Q: Explain the idea of cardinality. When is a set denumerable? Show that the union of two denumerable…

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Q: Do you think the set of all human beings and the set of all possible GPS coordinates have the same…

A: Both have the cardinality but not same cardinality  Cardinality is  refers to the relationship…

Q: Do the sets [0,1] and [0,1/2)∪(1/2,1] have the same cardinality? Either give an explicit bijection…

A: Yes, the sets 0,1 and 0,12∪12,1 have the same cardinality.

Q: State the cardinality of the set. {x|7 ≤ x ≤ 9}

A: Given that x|7≤x≤9To find : cardinality of the set.Solution :cardinality -cardinality  refers to the…

Q: Let A and B be infinite sets that are countable. Do A and B necessarily have the same cardinality as…

A: Given question is Let A and B be infinite sets that are countable. Do A and B necessarily have the…

Q: Match the following sets with their cardinalities. {t, 5, 1, p} Choose... {0} Choose... Choose... {}…

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Q: Give the cardinality of the set. (If the set has cardinality ℵ0, enter ALEPH NULL.) {47, 48, . . .…

A: Cardinality of a set is the number of elements in a set.

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

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Q: Give example for following 1/ set is not compact

A: Compact set:- A set S⊆R is called compact “if every sequence in S has a subsequence that converges…