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Q: [3.12] Let S be a nonempty convex set in R", and let f. R" → R be defined as follows:

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A: Consider the provided question, Suppose A and B are bounded, nonempty subsets of R.

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Q: Hw/ Find the foutier Seties of the periudic funtin %3D Ans/ 3. an-

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A: The solution is:

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Q: m) Show that if T;,T; and Ty are topologies on a set X.then r, nnt, is a topology on X.

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Q: 4. Suppose Rand S are symmetric relations on a set A. Prove that RoS is symmetric iff Ro S = So R.…

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A: Given: T and M are families of sets with T⊆M. To show: ∩T ⊆∪M

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Q: 5. Suppose that A and B are bounded subsets of R. Prove that AUB is bounded and that sup(AUB) =…

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A: The given question can be solved as shown in step 2 and 3. As per the guidelines of bartleby I'm…

Q: Let X = {a, b, c, d, e} and let T ={X, Ø, {a}, {c,d}, {a,c,d}, {b,c,d,e} }, then O XT) is neither…

A: Option 1 is correct.

Q: 4. Which sequence of transformations mapsAABC to ADEF? Are the image and preimage congruent? fy D F

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Q: a) Suppose that E is a set. If there exists a function f from E onto N, then E is at most countable.

A: (a) False f:E → INLet E= IR  Thenf: IR → INdefened as f(x) =  1  , ∨ x ∈ IRi.e There exist a…

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Q: Let N be with the discrete topology If A=(1,3,5..), then Bd(A)=

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Q: 3. Prove if x is an isolated point of a set S, then x E bd S.

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A: Given: F and G are two non-empty family of sets with F⊆G, To show: ∩F⊆∪G