(a) If {Ta} is a family of topologies on X, show that N Ta is a topology on X. Is UTa a topology on X?

Q: 4- A subset [a, b] R is compact set in: a- (R, Td), b- (R, T), c-Both (R, Tu) and (R, T₁) d- No one.…

A: As per our guidelines we are supposed to answer only first part. Kindly repost other parts in the…

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: 3. Determine if the matrik 4 is in the span of the set S = D

A:

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: 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: Show that compact sets are closed under arbitrary intersections and finite unions. (Here we're…

A: To show that compact sets are closed under arbitrary intersections and finite unions

Q: Let Gbe an open set in R". Two points x, y e G are said to be equivalent if they can be joined by a…

A: Since every open subset of Rn can be written of countable union of disjoint open balls and each ball…

Q: Exercise 1. Give examples of subsets A, B in a topological space X (for example X = R or X = R²)…

A: To give an example of subsets A,B in a topological space X such that both A,B are connected but A∪B…

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: Show this collection of subsets a partition of A UBUC {A – (B U C), B – (A U C), C – (A U B), ANBN…

A:

Q: Theorem 1.10. A set is infinite if and only if there is an injection from the set into a proper…

A:

Q: Theorem 1.14. The set of all finite subsets of a countable set is countable.

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}}

A:

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

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

Q: 4 ,3 ,2 ,1 = X آقا -X L find The Possible Topology That Contain sus { 1123 , 2, 3, {\/ 3 ، 4 seas

A: It is given that,  X = {1, 2, 3, 4}. We have to find the possible Topology on X that contain the…

Q: prove that i } X is a Coun table set and P: X>Y is asurjecbive then Y is Countable

A: Note: X denotes cardinality of X, that is number of elements in the set X. If X is countable means…

Q: Let A = {Ba: a € A} be a family of sets and let G be a nonempty set. Prove Gn an (UB.) - U(GOB₂) =…

A: Given: A=Bα : α∈∆ be a family of sets and let G be a nonempty set. To prove: G∩∪α∈∆Bα=∪α∈∆G∩Bα

Q: possible

A:

Q: Deteimine the set of vectuns sci, iti), (1tiyzi)f linealy dependent or linenly Indefendteut? is

A:

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

A: Topology Question

Q: Question 3. Consider the usual topology U on the set of real numbers. Describe the relative topology…

A:

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

A:

Q: ieN 5. (a) Uli,i+ 1]= (b) Nli, ieN ieN 6. (a) | Iro.i +11=

A:

Q: Encik Samsudin, a PhD student has reported the concentration of E.coli bacteria, C(μg/L) in a…

A: Given: C=kmaxt25+2t2+3.5t To find the root and to determine the fastest time for the E.coli…

Q: ☺ Let (u,Ue...,un) be a lineorly ndependent list. Which True Statement? is a has --- a non-zero…

A:

Q: i) Repeat the Cantor construction starting with the interval [0,1]. This time, however, remove the…

A: The cantor construction is to be done on the interval 0,1. To remove the middle fourth from the…

Q: Give an example of sets {An}n≥1 such that for each n ≥ 1, the set An ⊂ [0, 1] is both compact and…

A: Construct sets Ann≥1 such that for each n≥1, the set An⊂0, 1 is both compact and connected, but the…

Q: 4. [Falkner Section 15 Exercise 1 - modified] Show that the intervals A = [1, ∞) and B = (1, ∞) have…

A: In this case we define two segment. One for natural numbers and one for other numbers.

Q: what is the spanning fuzzy subgraph ? And give examples

A: We have to define fuzzy spanning subgraphs and give examples.

Q: Ris not connected if T is the trivial (usual) topology O the lower limit topology the indiscrete…

A: We know that

Q: how to use Bolzano Weierstrass Theorem to prove that every bounded infinite subset has at least one…

A:

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: Is it possible for two nonempty sets to have the same intersec-tion and union? If so, give an…

A: When two sets A and B overlap that is A = B, then the intersection and union of the  sets A and B…

Q: Compact sets.) Consider the set A = {-5} U [-3, 2]. Choose one of the three definitions of a compact…

A: A set S is called a compact set in ℝ if it is closed and bounded. using the above definition we will…

Q: open

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: I) We know that -5,-4,-3,-2,-1? and IN are well-ordered sets with respect to the trivial ordering.…

A: Solution: Given the sets -5,-4,-3,-2,-1 and ℕ are well-ordered with respect to the trivial ordering.…

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

A:

Q: Please poove 18 ŏ bound of (३5) fश्ठ also proove ppes an sup13,5)%35

A: (.) Upper bound:    "A number that is greater than or equal to any number in a non-empty subset of ℝ…

Q: an be cauchy, prove why a subsequence of (an) must also be cauchy.

A:

Q: what ordered pair is an example of a topological space that is connected but not path-connected,why?

A: We use contradiction method.