do any of them please??? Other Topologies on R. 1 he Michael Line. Letting tau d

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do any of them please???

Other Topologies on R. 1 he Michael Line. Letting tau denote the usual topology on R. define the topology tau by = is any subset of'R Q Show that Bm, = is a base for taum Show that, if a and b are both irrational, the interval (a.b) is both open and closed in taum.(If we restrict a and b to be irrational in the definition of Bm then Bm is still a base for taum. and so taum contains a base in which the sets arc all both open and closed. For this reason, the Michael Line (R. taum ) is said to be a zero-dimensional topological space.) If we let A = RQ, show that the relative topology tauA, on the Michael line is discrete. The Sorgenfiey Line. We let S = R with the topology sigma generated by the base of half-open sets beta = {[a,b): a

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just now i saw quest. i dont have enough time to solve it

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i dont guarantee but i will try

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