Let X be a set. Let Teof be the collection of subsets U of X such...

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Let X be a set. Let Teof be the collection of subsets U of X such that U is the empty set or X - U is a finite set. 1. If X is infinite, show that the topological space (X, Teof) is not metrizable. 2. What is Teof if X is a finite set? 3. Suppose that X = R. What is the relation between the cofinite topology Teof for X and the Euclidean topology TEuc for X? (Coarser? Finer? Neither?) Let X be a set. Let Teof be the collection of subsets U of X such that U is the empty set or X - U is a finite set. 1. If X is infinite, show that the topological space (X, Teof) is not metrizable. 2. What is Teof if X is a finite set? 3. Suppose that X = R. What is the relation between the cofinite topology Teof for X and the Euclidean topology TEuc for X? (Coarser? Finer? Neither?)

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