2- In a metric space (X, d), A is the intersection of all closed subsets of X which contains A.

Q: 5. If G1,G2 be two given closed sets in a metric space (X, d) prove that: G1 U G2 is closed.

A: We have to prove given result:

Q: Q7: Prove that (R", |l-|| ) is complete metric space.

A: This is a problem of Topology, Functional Analysis.

Q: 2.4.5. Let X be a metric space. Given x E X, prove that {x} is a closed subset of X.

A: Let (X,d) be a metric space to show that {x} is closed sunset of X.

Q: Prove that in a metric space (S,d) every closed ball Sr[Xo] is a closed set

A:

Q: The only subsets of R which are both open and closed under the discrete metric are Ø and R. Select…

A: This is False statement, in discreate metric space, every subset of R is both open as well as…

Q: Let (X, d) be a metric space and let A ⊆ X be complete. Show that A is closed.

A: Given that X,d be a metric space and A⊆X be complete. The objective is to show that A is closed.

Q: 3- In a complete metric space (X, d), If A C X such that, A = A then A is complete as a sub space of…

A:

Q: Let (X, d) be a metric space with X being a countable set. Show that X is not connected.

A: Let (X, d) be a metric space with X being a countable set. Show that X is not connected.

Q: 1) In a metric space (M, d), show that both Ø and M are open sets in M. 2) In a metric space (M, d),…

A: Open sets :- Let (M, d) be a metric space then a subset A of M is open if and only if each point of…

Q: 3.2 Prove that in any metric space (S.) every closed ball Se[xo] is a closed set.

A:

Q: 3. Prove that if G is an open set dense in the metric space (S, d) then SG is nowhere dense in S.

A:

Q: (a) Prove that every finite subset of a metric space is closed and has umulation points.

A: Since you have posted multiple questions, but according to guidelines we will solve the first…

Q: Let (X, d) be a separable metric space. into l∞.

A: This is a problem of functional analysis.

Q: If S is a closed bounded subset of a metric space X, then S is compact.

A:

Q: Let

A:

Q: Let A and B be any two subsets of a metric space (X, d). Then (1) A is a closed set. (2) If AC B,…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Theorem 8.6. Let C be a connected subset of the topological space X. If D is a subset of X such that…

A: Let C be a connected subset of the topological space X.Also given that D is a subset of X such that…

Q: Let A and B be any two subsets of a metric space (X, d). Then (1) A is a closed set. (2) If ACB,…

A:

Q: 1) In a metric space (M, d), show that both 0 and M are open sets in M. 2) In a metric space (M, d),…

A:

Q: Let (Ka)aeA be a collection of compact subsets of a metric space, X. Show naeAKa is closed in X.

A: A metric space X is compact if every open cover of X has a finite subcover.

Q: Let (X,d) be a metric space , x ϵ X and A ⊑ X be a nonempy set. Prove that d (x ,A) = 0 if and only…

A: Given: X,d is a metric space, x∈X and A⊂ X is a non-empty set. To Prove: dx,A=0 if and only if every…

Q: Prove that: 1. (R, |. |) is a complete metric space. 2. (Q.I-1) is not complete metric space.

A:

Q: 4. Let (X, d) be a metric space and xnx where each x, e X and x e X. Let A be the subset of X which…

A:

Q: 4. Let {Ka}aeA be a collection of compact subsets of a metric space, Show NaEA K, is closed

A:

Q: Show that any infinite subset A of a discrete topological space X is not compact.

A:

Q: (b) Show that the metric space (Q,1) is not complete. (c) Prove that the discrete metric space (M,d)…

A: Complete Metric Spaces :- A metric space (X, d) is said to be complete iff every Cauchy sequence in…

Q: 1) In a metric space (M, d), show that both 0 and M are open sets in M. 2) In a metric space (M, d),…

A: Open sets :- Let (M, d) be a metric space then a subset A of M is open if and only if each point of…

Q: 3. Let K,and K, be compact subsets of a metric space X. Show K, U K2 is compact

A:

Q: If x is a limit point of a subset A of a metric space X, then sh

A:

Q: Let (N, d) be the discrete metric space, then the set A = {2,3, 4} is closed but not open open but…

A:

Q: Prove that in any metric space (S, d) every closed ball S,[xo] is a closed set.

A:

Q: Q7: Prove that ( IR", ||·|| ) is complete metric space.

A:

Q: every finite subset of metric space is compact. ture or false?

A:

Q: (a) Prove that every closed subset S of a compact metric space (M,d) is compact in M.

A: Note: Our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: 1. Let M, d be a metric space with A C B C M. Suppose that B is totally bounded. Prove that A is…

A: Let (M, d) be a metric space and let A be a nonempty subset of M. The diameter of A is defined as…

Q: Prove the following: Let (Y, d) be a metric space. If Y is totally bounded, then Y is bounded.

A: Given:  (Y,d) is a metric space, and Y is totally bounded To Prove Y is bounded Definition: Let…

Q: Show that the closed ball Y in a metric space (x,d) is a closed set .Also show that if (x,d) is…

A:

Q: Q7: Prove that (R", ||-|| ) is complete metric space.

A:

Q: Prove that in any metric space (S, d) every closed ball S,[ro] is a closed set.

A: Use the following definitions, to prove the result. If a set contains all its interior points, then…

Q: Let M, be set of all rare subsets of a metric space X. Prove that countable union of M, is rare.

A: As per bartleby guidelines for more than one question asked only first should be answered. Please…

Q: Every closed subset of a connected metric space is connected. O True O False

A:

Q: Let (R, d) be discrete metric space and A = N then A is complete and compact neither complete nor…

A: Given that (ℝ,d) is a discrete matric space and A=ℕ. then     d(x,y)=0 if x=y1  if x≠y A matric…

Q: 4- For any closed subset A of a metric space, A' C A 5- In a metric space, the intersection of any…

A:

Q: 1- In a metric space (X, d), if A and A2 are open subsets of X then A1 U A2 is open in X. 2- In a…

A: Our guidelines we are supposed to answer only one question. Kindly repost other question as the next…

Q: Every closed subset of a connected metric space is connected. True False

A:

Q: Let X be ametric space. If A and B are each dense open subsets of X then AOB is dense open subset of…

A: First we have shown the intersection is open. Then we use the property that if a set intersect every…

Q: A metric space is said to be separable if it contains a countable dense subset. (a) Is R separable?…

A: Set of all rational numbers Q belongs to R and Q is dense in R . Also set of all rational numbers Q…

Q: 2) Let A be a closed bounded subset of a metric space (X, d). Is A a compact subset? Explain why.

A:

Q: (a) Prove that the metric space (Z,) is complete.

A: Complete Metric Spaces: A metric space (X,d) is said to be complete iff every Cauchy sequence in X…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.