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- Let X = {1, 2, 3, 4, 5, 6}. Prove that in general, if X is finite there is only one topology for X such thatX is T1. Please correct explanation.thanksare R is not connected if T is the indiscrete topology? Or if T is the trivial topology? Or if T is the finite closed topology?Please solve 2.26 .... so I have basically solved it but it but I need someone to show that there exists a topology T on N
- Solve 2.26 i posted this question an hour ago and somebody copied it from chegg, please don't do that don't simply say that T is a topology on N , prove it and show the steps plsProve that the first example is a topology and the second is not.Use the Heine-Borel Theorem to give an example of a noncompact set in R with the usual topology and a noncompact set R^2 with the usual topology. Please argue your answer. Thank you
- Give an example of a set in R^2 with the usual topology that is not connected but has a connected boundary. Please be as clear as possible and use definitions if necessary. Thank you a lotConsider X = {a1, a2, ..., an}Can a topology of X with 3 open and one with 4 open be equivalent?This is under Topology class:Answer thisa.) Show that if A is closed in Y and Y is closed in X, then A is closed in X.
- Recall that Rℓ denotes the Sorgenfrey line; that is, the set of real numbers with the topology generated by the basis {[a,b):a<b}. Determine whether or not Rℓ is connected. Justify your answer.Which of the following properties do you think are topological and why? a. Continuity. b. The symmetry. c. The connectedness d. linearity Justify and argue your answer. And the ones that are not whyIs R, equipped with the finite-closed topology, Hausdorff? Provide a proof supporting your answer.