Let X={a,b,c), then one of the fonowng is a base for some topology on X: O a. {{a,b),(b.c} O b. {{a).(a.c) Oc {a,b).(a.c).(a}} Od. ((a.b),(a.c).(b).(c)

Q: Let O be the collection of intervals Ia = (a, ∞) where a R along with I = 0 and I-∞ = R. Does this…

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Q: Let X={a,b,c,d}, then one of the following is a base for some topology on X: O a. {{a,b},{a,c},{a}}…

A: Base for a Topology If X is a set, then a base for a topology on X is a collection B of subsets of X…

Q: Let T be the Euclidean topology. Let A = [0,2] and B = [0,1[, then B is clopen in (A, TA) where TA…

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Q: 29. Let N be with the co-finite topology If A={1,3,5.), then Bd(A)=

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Q: * Let R be with the indiscrete topology. If A = {1,3, 5, 7, . }, then A' = A O N O RO

A: This question is related to topology, we will use the definition of indiscrete topology to solve it.

Q: Let T be the Euclidean topology. Let A = [0,1] and B =]0.5,1] then B is clopen in (A,T) where T is…

A: YOUR ANSWER IS True.

Q: Let R be equipped with the Euclidean topology T and let Y =]10,20[. We denote by Ty the induced…

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 3- Let X = {a, b} write a large Topology on X. 4- If A CX, find A' for (X.I).

A: (3) It is given that,  X = a, b. Then we have to write a large Topology on X. (4) It is given that,…

Q: Show that the dictionary order topology on the set R x R is the same as the product topology Rd × R,…

A: We have to show that the dictionary order topology on the set ℝ×ℝ is same as the product topology…

Q: the collection of all close subsets of R is called the topology of R

A: To check: Whether the statement is true or false: Given: The statement is "The collection of all…

Q: Which of the following is a topology on R? {UCR: U is infinite}U{U<R: U is countable} O {[a, b): a,…

A: We will use the definition of Topology.

Q: Let X = {1,2, 3, 4}. A topology on X is a. T = {6, X, {1}, {2}} b. T = {ó, X, {1}, {3,4}} c. T3 =…

A: Explanation of the answer is as follows

Q: Which of the following is not a base for any topology on R? a. {(a, b]: a,b ER and a <b} O b. {[a,…

A: Base for a topology: The base for topology of any set X is collection B of subsets of X which…

Q: I? B is a family of subsets of X Such that: (2) If B, ,BzE/ß them B,nB, EB Then B is a base for a…

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Q: 1. In R" where ne N, let B,(x) = {y: |x – yll 0) such that B,(x) C E} Show using the definition of…

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Q: Let X = {a, b, c, d}, S = {{a, b, c}, {a}, {b, c, d}}, and T be the topology on X generated by S.…

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Q: Let X = {a, b, c, d, e} and7 = {X,6. {a}. {c, d}, {a, c, d}, {b, c, d, e}} be a topology on X, then…

A: Details solution given below.

Q: Consider the set A=(x:x>a, a E R}U(x:xsb, bE R). Find the topology on R which has A as subbases.

A: Given :               Given a set                   A = x : x &gt; a, a∈R ∪ x : x ≤ b, b∈R     To…

Q: Let 7 be the Euclidean topology. Let A [0,2] and B [0,1, then Bis dopen in (AT) where 7, is the…

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Q: 3 let X= {ab,c},B =} {n,b}, {9c3}.5how that Whether B is a %3D %3D base for any topology on X or not

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Q: Let R be equipped with the Euclidean topology T and let Y =[10,20]. We denote by Ty the induced…

A: See the detailed solution below.

Q: Consider the set A=(x:x>a, a ER)U(x:xsb, bER). Find the topology on R which has A as subbases.

A: given a set  A=x:x&gt;a,a∈R∪x:x≤b,b∈R to find the topology on R which has A  as subbases

Q: Let τs and τ be the standard topology and the countable complement topology on R, respectively.…

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Q: 1) Let X be any non-empty set and xo E X. a) Prove that T = {X}U{AC X : xo ¢ A} is a topology on X.…

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Q: Let R be equipped with the Euclidean topology T and let Y =[10,20]. We denote by Ty the induced…

A:

Q: Let X = {1, 2, 3, 4} and T be the discrete topology on X. Consider the following statements: (a)…

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Q: Which of the following is not a base for any topology on R? O {(-0,a): a E (-∞, 0]}U{(0, ∞)} O {(a,…

A: Base for a topology: Let X, τ be a topological space. A collection of open sets B is said to be base…

Q: Let R be equipped with the standard topology. Define q : R? → R, q((x1, x2) : Jx1, if x1 2 x2 |X2,…

A: Question: The function q:ℝ2→ℝ defined by qx1,x2=x1, if x1≥x2x2, if x1&lt;x2 where ℝ2 and ℝ are…

Q: Let T be a topology on X. Assume that T is Hausdorff and let x € X. (1) Show that {x} (and hence…

A: let T be a topology on x. T is a Hausdorff space

Q: In a Cofinite topology of X the collection of subsets is: a) r = {AcX|A±Ø or A is finite} b) r = {Ac…

A: Let X be a non empty set , then the collection of subsets of X whose compliments are finite along…

Q: (a) Suppose M is a set and d, d' are two different metrics on M. Prove that d and d' generate the…

A: Please find answer below:

Q: The number of elements of the coc-countable topology on the set {a, b, c, d} is O 10 8 O 2 O 4 64 O…

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Q: * Let R be with the co-finite topology. If A = {1,3,5, 7,..}, then Aº R O Q O A O N O

A:

Q: Let X = {a, b, c, d, e} and t = {X, Ø, {a} , {c, d} , {a, c, d} , {b, c, d, e}} be the topology on X…

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Q: A topological space (X, t) is a T1-space iff t contains the cofinite topology on X.

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Q: Let Z be with the co-finite topology If A = {1,3,5, 7,.. }, then A A O O O

A: As Z is with co-finite topology. Every open neighborhood of an infinite set must contain infinitely…

Q: 3) let X be discrete topology and Ac X, find A ?

A:

Q: Let X = {a, b, c, d},S = {{a, b, c}, {a}, {b, c, d}}, and T be the topology on X generated by S.…

A: We  use the definition.

Q: 1) Let X be any non-empty set and xo E X. a) Prove that T = {X}U{ACX: 2o ¢ A} is a topology on X. b)…

A: Topology means we have to prove 3 conditions then we can tell that space is Topology.

Q: Consider R with the left ray topology. If A={2, 4, 8} the derived set of A is O a. (8, 00) Ob. A Oc.…

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Q: Let R be equipped with the Euclidean topology T and let Y =[10,20]. We denote by Ty the induced…

A: Let R be with Euclidean topology

Q: Let X = R, and let T consist of 0, R, and all intervals of the form (a, b) where a, b e R and a < b.…

A: A topological space is an ordered pair {\displaystyle (X,\tau ),} where {\displaystyle X} is a set…

Q: Let R be equipped with the Euclidean topology T and let Y =[10,20]. We denote by Ty the induced…

A: here option (c) is true because

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

A:

Q: Let R be equipped with the standard topology. Define q : R? → R, x1, if x1 2 x2 X2, if x1 < x2…

A: See the attachment

Q: Let X = {1, 2, 3, 4} and T be the discrete topology on X. Consider the following statements: (a)…

A: When T is the discrete topology of X, then it means Topology of T on X is the collection of all…

Q: Let X = (1, 2, 3, 4) and T be the discrete topology on X. Consider the following statements: (a)…

A:

Q: Let R be equipped with the Euclidean topology T and let Y =[10,20]. We denote by Ty the induced…

A: Induced topology

Q: Show that every covering of the Möbius strip is homeomorphic to either R², S¹ x R, or the Möbius…

A: We have to prove that every covering of the Mobius strip is homeomorphic to either R2or the strip…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.