Let A, B, and C are three sets, prove that B×(AnC)=(B× A)^(B×C)

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

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Q: We say that a space (X, τ) is not connected if there exist two nonempty openings A, B such that A ∩…

A: Open Set: A X, τ be a topological space. Then the sets in τ are called the open sets of the…

Q: Find a star in the radial plane topology that does not contain any rationals.

A: The objective is to find the star in the radial plane topology which does not contain any rationals

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: Find example where of is continuous and an - bijective but f¹ is not

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Q: How many different functions are there from a set with 10 elements to sets with 2 elements?

A: Definition 1.Function : A relation where every input has one single output. 2.Product rule: If one…

Q: State the Squeeze Theorem carefully.

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Q: What is norm space

A: In mathematics, a normed space or a normed vector space is a vector space over the real or complex…

Q: Determine whether the points are coplanar.(1, −5, 9), (−1, −5, 9), (1, −5, −9), (−1, −5, −9)

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Q: Be M, N subsets of space W. Then span (MUN) = span (M) +span (N)- %3D

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Q: If (X.r) and (X,r,) are T,-spaces, then (X.r,nt) is also a T, -space. GOOD LUCK

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Q: If X and Y are separable spaces, then X × Y is separable.

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Q: Show the span {(1,0, 1), (-1, 2, 3), (0, 1, – 1)} is all of R'.

A: Let x=1, 0, 1, y=-1, 2, 3 and z=0, 1, -1. We have to show that spanx, y, z is actually the vector…

Q: rsection of any collection of com

A: This is a real analysis question. Let (X,d) be a complete metric space with X not ∅. Suppose the…

Q: With the help of exomples Show thaat on finite dimensional are equivalent. any two norms Linear…

A: Given: Any two norms on finite dimensional linear space are equivalent.

Q: give example is not To-SPace about to folegical SPace

A: We have to find a topological space which is not t0.

Q: How many different functions are there from a set with 10 elements to sets with 5 elements?

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Q: The cartesian product of nonempty family of nonempty sets is nonempty صواب ihi

A: The cartesian product of nonempty family of nonempty sets is nonempty

Q: How many onto functions are there from a set with six elements to a set with four elements?

A: Formula: If a set A contains m elements and a set B contains n elements then number of onto…

Q: A and the set B = {x, y}, then A X B is denumerable as well.

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Q: Classify the discontinuity of as a removable, jump or infinite?

A: This question is related to continuity and differentiability.

Q: denotes the set of subsp

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Q: Let X And Y be two distrecte spaces. Then X is homeomorphic to Y if and only if X and Y are both…

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Q: If (X.r,) and (X,r,) are T.-spaces, then (X.r,nr,) is also a T,-space. GOOD LUCK

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Q: Verify the relations (5).

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Q: Let matices

A: Given that, I=1001 ; A=100-1 ; B=-1001 ; C=-100-1 G = {I, A, B, C} Let the binary operation defined…

Q: Find the value of t for which (4, 6, 3, t) belongs to Span {(1, 3, -4, 1), (2, 8, -5, -1), (-1,…

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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: umat is bounded, and is not compact in Q.

A: Here the closed means closed with respect to subspace topology. And compact means every cover has…

Q: is this a fucntion or not. given its domain and range   {(1,1), (2,2), (3,3), (4,4)}

A: This is a function.

Q: What is the minimum number of points that can be contained in a space

A: There is no minimum number of points to be contained in a space. But if we want to find a location…

Q: If (X,7,) and (X,7,) T. - spaces, then (X,7,nt) is also a T,- space. GOOD LUCK

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Q: Express the set using the Roster Method: {x|x X eN and x)53

A: GIVEN XX∈N and  X>5

Q: Let ū, ů ů be VCctors in a real inner Product spale, with cŮ, w) = -3 (ů,3) =5 ニ 11ů-20112 -(25, ) =…

A: Given: u→.v→=2, v→.w→=-3, u→.w→=5, u→=3, v→=2, w→=2 we know that u→-2v→2-2w→.w→ is given by…

Q: Suppose the operators Å and B are projection operators. Show that the sum of two projection…

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Q: Give an example of a norm space.

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Q: Show that topologically completeness is weak hereditary property.

A: In this question, we have to show that completeness is a weak hereditary property.

Q: If A and B are distinct points in 3-space then |AB| = - Select one: True False

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Q: Show that closed ball in metric space (x,d) is a closed set. Also,

A: Given: (x,d) is a metric space The objective is to show that the closed ball y in (x,d) is a closed…

Q: Prove that the smallest member of a set, if exits, is the greatest lower bound of the set. Correct…

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Q: Find the bounded of the determine red In the same way as the proof of theorem 4 in the second…

A: Given:                                            Sn+1=Sn-paSn-q+bSn-r+cSn-sdSn-q+eSn-r+fSn-s…

Q: ind the all possible number of different multi sets of size '4' from -element set, in which at least…

A: In this question, the concept of permutation is applied. Permutation Permutations are frequently…

Q: ) Find an example of an infinite collection of closed sets whose union is not closed.

A: Any closed interval is closed in R. From that we created this example.

Q: Let (X, τ ) be a discrete space. Is (X, τ ) second countable? Explain why

A: Consider the provided question, Let x,τ be a discrete space,    ⇒x,τ  be denote topology if x,τ is…

Q: Show That R is Banach Sface.

A: To Show -

Q: Find two examples for equivalet norms on three dimensional real space

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Q: Compute the adjoint of the foll

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

Q: Show that the closure of a connected space is connected.

A: