Let X be an infinite set with the finite closed topology T={S subset of X; X-S is finite). Then" O XT)Is homeomorphic to (X,T1) where T1 is the finite closed topology on X O None of the choices, O Every Infinite subset ofX is dense in X OXT) Is not T1 space

Q: Let A and B be bounded NON empty sets of R, and let A + B := { a+b: at A, bt B3. Prove that supla…

A:

Q: Let's say that a collection of open balls (Ui)ie1 = (Bx, (ri))iel in Euclidean space Rd is = UB₂,…

A:

Q: Theorem 2.1. Let{U}{_, be a finite collection of open sets in a topological space (X,T). Then N, U…

A:

Q: (i) Show that a subset A of a topological space X is closed if and only A = A (ii) Prove that A…

A:

Q: The connected components of a space X are all the maximal connected subsets with respect to…

A:

Q: Let Y be an infinite subset of a compact set XC R. Prove Y' 0.

A:

Q: Theorem 7.42. The Cantor set is homeomorphic to the product InEN{0, 1} where {0, 1} has the discrete…

A: Given: The Cantor set and the product topology on the set ∏n∈N 0,1, where 0,1 has the discrete…

Q: Let x be non-empty of points. a topological Space having open set with finite numb cal shase wh

A: Let X be a topological space having non-empty open set with finite number of points. Let Y be a…

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

A: Connected means it cannot be written as union of disjoint open sets