Regular topological spaces

Reference no: EM13135296

a) Reals with the "finite complement topology:" U open in X if U - X is finite or is all of X. Why compact? Why not regular?

b) Reals with the "countable complement topology:" U open in X if X - U is countable or is all of X. Why not compact? Why not regular.

c) Reals with the "K-topology:" basis consists of open intervals (a,b) and sets of form (a,b) - K where K = {1, 1/2, 1/3, ... } Why not compact? Why not regular?

Reference no: EM13135296

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