Let X be an infinite set T be topology of the a Linfinite subsets that is on x- and let on X in which all Show X are open. discrete topology t

Q: Let τ and τ' be two topologies of a set X. Is the family τ∪τ' formed by the open elements of both…

A: Union of two topologies is not necessary a topology.

Q: d) K, has an Eulerian circuit for every natural number n 2 3. e) Every finite poset has a minimal…

A: d)

Q: A topological space is Hausdorff iff limits of all nets in it are unique

A: This is a problem of Topology.

Q: Let X be an infinite set with the countable closed topology T={S subset of X; X-S is countable).…

A:

Q: Suppose S be an open connected subset in arbitrary topological space X. Whether S is path connected…

A: If S is an open connected subset of a topological space X, then it is path connected. A subset S of…

Q: Let T = {0, En}, where En = {n +1, n + 2, n + 3, ...} with n E N, be a topology on N. Then the set…

A: Ans : False , because

Q: Evaluate the expression a+b a+b when a=23a=23 and b=45b=45. Write in simplest form

A: # the expressions are printed twice , taking them once given a=23 and b=45 The value of a+b is as…

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: Let T be the finite closed topology on a finite set X, then * O Tis the Euclidean topology O Tis the…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: An indexed family of sets (Ahess said te be a cover of a set X tand only i X CUEIA Use this idea to…

A: Let C and D be two different indexed family of sets Ci and Dj. Then C=Ci:i∈ID=Dj:j∈J Suppose C and D…

Q: (b) Show that the continuous image of compact set is compact but the convers need not to be true.…

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Q: UNA annetect in X show that Tivi is a connected set in a space Y. ) Let T be a cofinite topology…

A: If  X is a non-empty set, then the collection of subsets of X whose complements are finite along…

Q: let x be an infinite set and let ta be a topology on x in which all infinite subsets of x are open…

A: Given that X be an infinite set and let τ be a topology on X in which all infinite subsets of X are…

Q: Let ∼ ⊆ X ∗X be an equivalence relation on a set X. For x ∈ X define ̄x := {y ∈ X |x ∼ y}. Then it…

A:

Q: (1) Let X be a set and tEX, let t={GCX/ t€G or G° finite }, show that whether t is a topology on X…

A:

Q: Let X be an infinite set T be topology infinite subsets of that is on X- and let on X in which all…

A: Given :  X be an infinite set and τ be a topology on X such that all the infinite subsets of X are…

Q: y = - 1.5 cos (3x -90) +0.5   what is the    a) period  b) amplitude  c) the phase shift

A: Since you have uploaded multiple part questions according to our guidelines we have solved the first…

Q: Let X be an infinite set and T a topology on X. If every infinite subset of X is in T, prove that T…

A:

Q: Consider a set X = {a,b} as a topological space with a discrete topology. Let J be an uncountable…

A: We will use basic knowledge of results and definitions of general topology.   We claim that Z is NOT…

Q: Let X be a non empty set and p be a fixed point in X. Define T={X, ACX such that p€A}. Then any…

A:

Q: Show that there is no topology on X={a,b,c,d,e} based on the family B={{a,b},{a,b,d},{b,d,e}}

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Q: (3) X is not the union of two disjoint non-empty separated sets. (4) X is not the union of two…

A: as given all the conditions are equivalent  (4) To show - X is not the union of two disjoint non…

Q: xercise 2. Show that a set with the discrete topology is compact if and only if it is finite. if and…

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Q: Which one of the following statements is true? * R with the Euclidean topology and R with the…

A: Two homeomorphic spaces share the same Topological property If one of them is compact, then the…

Q: Given a finite set S, find all possible values of |S] so that the set {(a, b) | (a E S) A (b e S) ^…

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Q: Q1.Consider X ={a,b, c, d, f, g} .Let T={ó, X, {a,b, c} ,{g};{a,b, c, g}} (a) Prove that T is a…

A: Since you post a question with multy part, we solve only first three, if you need any particular…

Q: Hausdorff space.

A: Given: A set X with co-finite topology and  Hausdorff space. To Find: Under what condition a set X…

Q: (a) When is a subset of a topological space said to be closed? (b) Fotmulate the definition of…

A: If X,𝞽 is a topological space, then a closed set in X is a subset of X whose complement is a member…

Q: Prove that closed balls are closed sets in the standard topology on R?.

A: Topology Question

Q: Which one of the following statements is true?

A: In the R with the Euclidean topology and R with the finite closed topology, f might not be…

Q: shows that there is no topology in X based on the family B = {{a, b}. {a, b, d}, {b, d, c}}

A:

Q: Show that the collection of all sets which are union of sets of the form [a, b) is a topology on R.

A: To Show: The collection of all sets which are the union of sets of the form [a, b) is a topology on…

Q: 1) Let Xbe an infinite set with the Finite Complement Topology. Let A EX be an infinite subset.…

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Q: Show that if a topological space has a finite number of points each of which is closed then it has…

A: Topology question.

Q: Let T and T 'be two topologies of a set X. Is the family T U T´formed by the openings common to both…

A:

Q: Ris not connected if T is * O None of the choices O the trivial (usual) topology the indiscrete…

A: R is not connected if T is

Q: How can I show that the collection  A composed of empty set and all cofinite subsets of X Is a  sets…

A:

Q: Let X = {1, 2, 3, 4, 5, 6}. Prove that in general, if X is finite there is only one topology for X…

A: Let X = {1, 2, 3, 4, 5, 6}. Prove that in general, if X is finite there is only one topology for X…