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

Q: i. PROVE THAT THE EXCLUDED POINT TOPOLOGY ON ANY SET WITH AT LEAST 2 POINTS IS NOT HAUSDORFF. ii.…

A: Definition: A topological space X, τ is said to be Hausdorff if for every x, y∈X there exits U, V∈τ…

Q: Define Open set ?

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Q: When is a set compact?

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Q: For all sets A B and c, of CAXC)- CBrC)# Ø, then A-B#¢.

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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: The universal set is U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. If A = {1, 2, 3, 4, 5} and B = {4, 5, 6,…

A: It is given that the universal set is U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.If A = {1, 2, 3, 4, 5} and…

Q: Show

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

Q: Let U = {a,b,c,d,e,f,12,13,14,15,16,17}, X = {a,b,c,15,16,17), and Y = {b,d,f,13,15,17}. List the…

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Q: If a universal set contains 250 elements,

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Q: a) State the intersecton of an indexed family of sets.

A: According to guidelines we can do only first question thank you .we have to state the intersecton…

Q: (b) Let = {A; : i EN} be an indexed family of sets with the property that A₁ A₂ 22 A, 2..., that is,…

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Q: Prove T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set

A: We have to prove the following -   T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set.

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: Prove that an enumerable set is infinite.

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Q: open

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Q: 3.) Nowe consider motrix cif possible) as a linear combination of the motrices in' ls. the set s…

A: Given that: S=3-333,3-245,6-3106To express the the following matrices in the linear combination of…

Q: Construct an example of a subset B of p({a, b, c, d}) such that (B, C) is a totally ordered set.

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

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Q: Suppose that U1, U2, ..., Un is a collection of n open sets. Prove that their intersection…

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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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