umat is bounded, and is not compact in Q.

Q: Show that every second countable (A2-space) space is separable.

A:

Q: Use induction to prove that the number of elements in any SList of depth p is 2P.

A: We have to prove that the number of elements in any SList of depth p is . Notice that the…

Q: Suppose A and B be subsets of metric space. Show that if A is compact and B is closed then A + B is…

A: Given A and B are subsets of a metric space. and also Given A is compact , and B is closed. We have…

Q: Show with all the relevant details, albeit succinctly that every compact metric space M is complete.

A: Here we use sequential definition of compactness so that we use that in proving the completeness of…

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

A: A set is said to be infinite countable if its elements can be counted like natural number but you…

Q: Assume that A and B are nonempty, bounded above, and satisfy B CACR. Show that sup B < sup A.

A: Introduction: The supremum and infimum properties are the very important properties of any subset of…

Q: Show that the space (P is complete.

A: The given problem is to show that the space lp is complete. we can use properties of lp spaces to…

Q: We define the included point topology by Tp={ UCR;U=Ø or pEU}. Let A = [3,5[, then A is dense in Rif…

A:

Q: 2. if it was P(x)=ao+a,%tazk Prove that PecR) inner multiPlication sPace

A:

Q: let A be a bounded. Sup A non. n-empty set in R show that is a limit point of A.

A:

Q: Suppose A ⊂ R is both closed and bounded, prove that A has the Heine-Borel Property

A:

Q: Every closed and bounded subset of X is compa The subset {z EX: |||| ≤ 1} of X is compact... X is…

A:

Q: Show that the following PDE is separable: tur + xu = 0

A: In this question, we solve the partial differential equation by separation of variable as…

Q: Give an example of a metric space X, d and a sequence {Pn} C X such that {pn} is a Cauchy sequence…

A: Let X=(0,∞) Define d:X×X→ℝ+∪0 by d(x,y)=x-y.i.e. d is a standard metric on X induced from ℝ.Take…

Q: A normed space X overR is separable if it has a conutable dense subset 0 صواب ihi

A: The given statement that " A normed space X over R is seperable if it has a countable dense subset "…

Q: Prove that a square maximizes the area of all rectangleswith perimeter P.

A:

Q: Show that recel projeetrue space is an manifol a.

A:

Q: 4. Show that =N} which is subset of R is not compact by describing an open cover for n it that has…

A:

Q: prove that an is bounded above.

A: In this question, we prove the sequence  an=(1+1n)n is convergent by given porcedure. i.e.…

Q: show that (0.1)with usual topology is connected

A: Sol

Q: We define the included point topology by Tp={UCR;U=Ø or pEU}. Let A = [3,5[, then A is dense in R if…

A: The detailed explanation is given below:

Q: (K", || |,) is called the LP-norm on K". is a normed linear space for 1 <PS00. || |,

A:

Q: Every connected subset of R is complete is ture or false?

A: Every connected subset of R is complete is true or false?

Q: What is the norm of a partition of a closed interval?

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: ket (X, @) be a topokgical space, Ka compact subset of X and (FalneN a family in PCX) with Fr+ Ø POR…

A:

Q: Show that the compactness in satability theorem is neccessary.

A: The Stability Theorem fails when X is not compact

Q: The set S=[1,3) is not compact. Which open cover of S contains a finite subcover?

A: This is the question of Topology.

Q: Without appealing to Heine-Borel, prove that [0, 1] CR is compact and connected in the standard…

A: Please check in the next step

Q: Describe the largest set S on which it is correct to say that fis continuous. AX, y) = In(1 + x² +…

A:

Q: Let S be a non-empty open subset of R that is bounded above. Show that sup S exists but that max S…

A:

Q: If A and B are nonempty bounded subsets of R with A C B, prove that sup A < sup B.

A:

Q: If A and B are bounded subsets of R, then AuRand AOR are bounded: prove that

A:

Q: Prove that ℝ with lower limit topology is Hausdorff

A: Solution :-

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: Prove by sequences that the open balls in R^n with the usual (Euclidean) metric are not compact

A: In this question, we have to show that open balls in ℝn with the usual metric are not compact by the…

Q: Use the Heine-Borel theorem to show that every closed and bounded interval [a, b] with the absolute…

A: Compact Set: A collection A of subsets of space X is said to be cover X or covering of X if the…

Q: Let {an} and {bn} be bounded above. State hypotheses which guarantee {anbn} will also be bounded…

A:

Q: 4. Use the least upper bound property of R to prove that every nonempty subset of R that is bounded…

A: Solution

Q: Show that all open balls are bounded subsets of a metric space.

A: Solution: Let M=X,d be a metric space. For an arbitrary point a∈X, the open ball Bεa where ε&gt;0 is…

Q: Show that the compactness in satability theorem is neccessary

A: Stability Theorem :- The following classes of smooth maps on a compact manifold X in to Y are stable…

Q: Prove disprove that (R.Tco-finite) is Te-space or

A: To Prove - Prove or Disprove that ℝ, τco-finite  is T2 - space.       Definition used - T2 - space…

Q: Consider the topology 7 = {GCR:0 ¢G or G = R} on R. Is open interval (-1, 1) compact in (R, T)?…

A:

Q: Prove that if g′ is bounded on (a, b) then g is uniformly continuous on (a, b).

A:

Q: Since, F is bounded both in LOR) and in lIR), it is Latnded in LLIR) forall fe[1,0) (Prdtem 31).

A:

Q: If o + SCR is bounded above, then S has a supremum. Select one: True False

A:

Q: Exhibit an open cover of the interval (1, 2] that has no finite subcover.

A: An open cover of A is a collection of open subsets of A whose union is all of A and that a finite…

Q: let FQ) = -2Xidefined on [14], then UC Pmif) =

A:

Q: Suppose metric space X is not path-wise connected then X is not connected. True False

A: A space is said to be Path connected if we can fine a continuous function between any two points of…

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.